Skip to main content
Back to TRIGONOMETRY RATIOS

Your Progress

0 / 394 Answered
0
Correct
0
Incorrect
0%
Accuracy
JEE • MATHEMATICS • TRIGONOMETRY RATIOS

Trigonometry ratios practice · Mixed difficulty

Choose an answer to check it, or open “View answer” to study the explanation. Sign in to save progress to your account.

Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

Take a chapter quiz →
Showing 361-390 of 394 questions

Preparing practice and saved progress…

361 Easy
361 of 394
Application +4 | -1
If tan⁡θ=17\tan \theta=\frac{1}{\sqrt{7}}, then (cosec⁡2θ−sec⁡2θcosec⁡2θ+sec⁡2θ)\left(\frac{\operatorname{cosec}^2 \theta-\sec ^2 \theta}{\operatorname{cosec}^2 \theta+\sec ^2 \theta}\right) is equal to mm+1\frac{m}{m+1}. The value of mm is
View answer and explanation
Correct option: A
3
Option A (1) is correct because evaluating the given expression using the values of trigonometric functions at the specified angles results in 1.
362 Easy
362 of 394
Application +4 | -1
If sin⁡  θ+cosec    θ=2\sin \,\,\theta + \mathrm{cosec}\,\,\;\theta = 2, the value of sin⁡10  θ+cosec10  θ{\sin ^{10}}\,\,\theta + \mathrm{cose}{\mathrm{c}^{10}}\,\,\theta is
View answer and explanation
Correct option: A
2
Option A is correct because when sin θ + cosec θ = 2, it implies sin θ = 1, and thus sin¹⁰ θ + cosec¹⁰ θ = 1 + 1 = 2.
363 Medium
363 of 394
Application +4 | -1
If p=2sin⁡θ1+cos⁡θ+sin⁡θp=\frac{2 \sin \theta}{1+\cos \theta+\sin \theta}, and q=cos⁡θ1+sin⁡θq=\frac{\cos \theta}{1+\sin \theta}, then
View answer and explanation
Correct option: D
q+p=1q+p=1
Option D (q+p=1q+p=1) is correct because the given expressions for pp and qq can be simplified using trigonometric identities to show that their sum equals 1.
364 Easy
364 of 394
Understanding +4 | -1
The value of the expression cos  1∘  .  cos⁡  2∘…..cos⁡  179∘\mathrm{cos}\,\,1^\circ \,\,.\,\,\cos \,\,2^\circ \ldots ..\cos \,\,179^\circ equals
View answer and explanation
Correct option: A
0\mathrm{0}
Option A (0) is correct because the product includes cos(90°), which is 0, making the entire product 0.
365 Medium
365 of 394
Application +4 | -1
In a △ABC, a2sin⁡2B+b2sin⁡2A\triangle {ABC}, \, {a}^2 \sin 2 {B}+{b}^2 \sin 2 {A} is equal to (where Δ\Delta is area of △ABC\triangle {ABC})
View answer and explanation
Correct option: A
4Δ4 \Delta
Option A (4Δ4 \Delta) is correct because a2sin⁡2B+b2sin⁡2Aa^2 \sin 2B + b^2 \sin 2A simplifies to 4Δ4 \Delta using trigonometric identities and the area formula.
366 Medium
366 of 394
Analyzing +4 | -1
sin⁡2  θ=4 xy(x+y)2{\sin ^2}\,\,\theta = \frac{{4\,xy}}{{{{\left( {x + y} \right)}^2}}} is true if and only if
View answer and explanation
Correct option: B
x=y,  x≠0,   y≠0x = y,\;x \ne 0,\;\,y \ne 0
Option B (x=y,  x≠0,   y≠0x = y,\;x \ne 0,\;\,y \ne 0) is correct because the equation holds true only when x and y are equal and non-zero, ensuring that the sine squared value is less than or equal to 1.
367 Easy
367 of 394
Application +4 | -1
The value of cot⁡54∘tan⁡36∘+tan⁡20∘cot⁡70∘\frac{\cot 54^{\circ}}{\tan 36^{\circ}}+\frac{\tan 20^{\circ}}{\cot 70^{\circ}} is
View answer and explanation
Correct option: B
2
Option B (2) is correct because cot⁡54∘=tan⁡36∘\cot 54^{\circ} = \tan 36^{\circ} and tan⁡20∘=cot⁡70∘\tan 20^{\circ} = \cot 70^{\circ}, so the expression simplifies to 1 + 1 = 2.
368 Easy
368 of 394
Application +4 | -1
The product (cos⁡x2)⋅(cos⁡x4)⋅(cos⁡x8)⋯⋯⋅(cos⁡x256)\left(\cos \frac{x}{2}\right) \cdot\left(\cos \frac{x}{4}\right) \cdot\left(\cos \frac{x}{8}\right) \cdots \cdots \cdot\left(\cos \frac{x}{256}\right) is equal to:
View answer and explanation
Correct option: B
sin⁡x256sin⁡x256\frac{\sin x}{256 \sin \frac{x}{256}}
Option B (sin⁡x256sin⁡x256\frac{{\sin x}}{{256 \sin \frac{{x}}{{256}}}}) is correct because repeatedly multiplying and dividing by sine terms and using the identity sin⁡2θ=2sin⁡θcos⁡θ\sin 2\theta = 2 \sin \theta \cos \theta leads to the given expression.
369 Easy
369 of 394
Application +4 | -1
If tan⁡A−tan⁡B=12\tan A-\tan B=\frac{1}{2} and cot⁡A−cot⁡B=13\cot A-\cot B=\frac{1}{3}, then cot⁡(A−B)\cot (A-B) is equal to:
View answer and explanation
Correct option: B
-1
The correct answer is B (-1) because by manipulating the given equations and using the cotangent subtraction formula, we find the value of cot(A-B).
370 Easy
370 of 394
Application +4 | -1
The expression 3  {sin⁡4(3 π2−α)+sin⁡4  (3 π−α)}−2  {sin⁡6(π2+α)+sin⁡6  (5 π−α)}3\,\,\left\{ {{{\sin }^4}\left( {\frac{{3\,\pi }}{2} - \alpha } \right) + {{\sin }^4}\,\,\left( {3\,\pi - \alpha } \right)} \right\} - 2\,\,\left\{ {{{\sin }^6}\left( {\frac{\pi }{2} + \alpha } \right) + {{\sin }^6}\,\,\left( {5\,\pi - \alpha } \right)} \right\} is equal to
View answer and explanation
Correct option: B
1\mathrm{1}
Option B (1) is correct because after simplifying the trigonometric expressions and applying trigonometric identities, the expression evaluates to 1.
371 Medium
371 of 394
Analyzing +4 | -1
The value of the expression 1−sin⁡2  y1+cos⁡  y+1+cos⁡  ysin⁡  y−sin⁡  y1−cos⁡  y1 - \frac{{{{\sin }^2}\,\,y}}{{1 + \cos \,\,y}} + \frac{{1 + \cos \,\,y}}{{\sin \,\,y}} - \frac{{\sin \,\,y}}{{1 - \cos \,\,y}} is equal to
View answer and explanation
Correct option: D
cos⁡  y\cos \,\,y
Option D (cos y) is correct because the expression simplifies to cos y after applying trigonometric identities and algebraic manipulation.
372 Easy
372 of 394
Application +4 | -1
If cosec⁡θ=p+qp−q\operatorname{cosec} \theta=\frac{p+q}{p-q}, then cot⁡(π4+θ2)=\cot \left(\frac{\pi}{4}+\frac{\theta}{2}\right)=
View answer and explanation
Correct option: B
qp\sqrt{\frac{q}{p}}
Option B (qp\sqrt{\frac{{q}}{{p}}}) is correct because after applying componendo and dividendo and simplifying, cot⁡(π4+θ2)=qp\cot(\frac{{\pi}}{{4}} + \frac{{\theta}}{{2}}) = \sqrt{\frac{{q}}{{p}}}.
373 Medium
373 of 394
Application +4 | -1
If   tan⁡  A+sin⁡  A=m    and  tan⁡  A−sin⁡  A=n  \;\tan \,\,A + \sin \,\,A = m\,\,\;\mathrm{and}\,\,\tan \,\,A - \sin \,\,A = n\; then (m2−n2)2mn\frac{{{{\left( {{m^2} - {n^2}} \right)}^2}}}{{mn}} is equal to
View answer and explanation
Correct option: C
16
Option C (16) is correct because it is the simplified value of the expression after substituting the given equations and using trigonometric identities.
374 Medium
374 of 394
Application +4 | -1
The value of sin⁡  π16  sin⁡  3π16  sin⁡  5π16  sin⁡  7π16\sin \,\,\frac{\pi }{{16}}\,\,\sin \,\,\frac{{3\pi }}{{16}}\,\,\sin \,\,\frac{{5\pi }}{{16}}\,\,\sin \,\,\frac{{7\pi }}{{16}} is
View answer and explanation
Correct option: A
216\frac{{\sqrt 2 }}{{16}}
Option A (216\frac{{\sqrt 2 }}{{16}}) is correct because the product of the sines can be simplified using trigonometric identities to obtain this value.
375 Easy
375 of 394
Application +4 | -1
Let f(x)=17−sin⁡5xf(x)=\frac{1}{7-\sin 5 x} be a function defined on RR. Then the range of the function f(x)f(x) is equal to:
View answer and explanation
Correct option: D
[18,16]\left[\frac{1}{8}, \frac{1}{6}\right]
Option D ([18,16]\left[\frac{{1}}{{8}}, \frac{{1}}{{6}}\right]) is correct because it represents the range of the function, determined by considering the minimum and maximum values of the sine function.

Explore Other Chapters in MATHEMATICS

View All →
SEQUENCE OF SERIES 1764 MCQs DEFINITE INTEGRATION 1443 MCQs MATRICES 1363 MCQs INDEFINITE INTEGRATION 1179 MCQs PROBABILITY 1146 MCQs COMPLEX NUMBERS 980 MCQs
376 Easy
376 of 394
Application +4 | -1
If sin⁡(x−y)=cos⁡(x+y)=12\sin \left( {x - y} \right) = \cos \left( {x + y} \right) = \frac{1}{2}, the values of x\mathrm{x} and y\mathrm{y} lying between 0∘0^\circ and 90∘90^\circ are given by
View answer and explanation
Correct option: D
x=45∘,   y=15∘x = 45^\circ ,\;\,y = 15^\circ
Option D (x=45∘,   y=15∘x = 45^\circ ,\;\,y = 15^\circ) is correct because these values satisfy both given equations sin⁡(x−y)=1/2\sin(x-y) = 1/2 and cos⁡(x+y)=1/2\cos(x+y) = 1/2.
377 Easy
377 of 394
Application +4 | -1
If sin⁡Asin⁡B=32\frac{\sin A}{\sin B}=\frac{\sqrt{3}}{2} and cos⁡Acos⁡B=52\frac{\cos A}{\cos B}=\frac{\sqrt{5}}{2}, 0<A,B<π/20 < A, B < \pi / 2, then tan⁡A+tan⁡B\tan A+\tan B is equal to
View answer and explanation
Correct option: D
(3+5)/5(\sqrt{3}+\sqrt{5}) / \sqrt{5}
Option C (136,116\frac{{13}}{{6}}, \frac{{11}}{{6}}) is correct because it satisfies both equations in the system.
378 Easy
378 of 394
Understanding +4 | -1
In a triangle ABCA B C the value of sin⁡A+sin⁡B+sin⁡C\sin A+\sin B+\sin C is
View answer and explanation
Correct option: B
4cos⁡A2cos⁡B2cos⁡C24 \cos \frac{A}{2} \cos \frac{B}{2} \cos \frac{C}{2}
Option B (4cos⁡A2cos⁡B2cos⁡C24 \cos \frac{A}{2} \cos \frac{B}{2} \cos \frac{C}{2}) is correct because it is the result of applying trigonometric identities to simplify the expression sin⁡A+sin⁡B+sin⁡C\sin A + \sin B + \sin C.
379 Easy
379 of 394
Application +4 | -1
tan⁡2θ+cot⁡2θ1\tan ^2 \theta+\cot ^2 \theta{ }_1. Is
View answer and explanation
Correct option: A
≥2\geq 2
Option A (≥2\geq 2) is correct because by using the AM-GM inequality or by considering the square of the difference, it can be shown that tan⁡2θ+cot⁡2θ≥2\tan^2 \theta + \cot^2 \theta \geq 2.
380 Medium
380 of 394
Remembering +4 | -1
∑n=124sin⁡(π2)\sum_{n=12}^4 \sin \left(\frac{\pi}{2}\right) is equal to
View answer and explanation
Correct option: D
3+2+22\frac{\sqrt{3}+\sqrt{2}+2}{2}
Option D (3+2+22\frac{\sqrt{3}+ \sqrt{2}+2}{2}) is correct because it is the sum of sin⁡π1\sin{\frac{\pi}{1}}, sin⁡π2\sin{\frac{\pi}{2}}, sin⁡π3\sin{\frac{\pi}{3}}, and sin⁡π4\sin{\frac{\pi}{4}}.
381 Easy
381 of 394
Application +4 | -1
cos⁡10∘+sin⁡10∘cos⁡10∘−sin⁡10∘\frac{\cos 10^{\circ}+\sin 10^{\circ}}{\cos 10^{\circ}-\sin 10^{\circ}} is equal to
View answer and explanation
Correct option: A
tan⁡55∘\tan 55^{\circ}
Option A (tan⁡55∘\tan 55^{\circ}) is correct because the expression simplifies to tan⁡(45∘+10∘)\tan(45^{\circ} + 10^{\circ}) using the tangent addition formula.
382 Easy
382 of 394
Application +4 | -1
cos⁡2(π6+θ)−sin⁡2(π6−θ)=\cos ^2\left(\frac{\pi}{6}+\theta\right)-\sin ^2\left(\frac{\pi}{6}-\theta\right)=
View answer and explanation
Correct option: A
12cos⁡2θ\frac{1}{2} \cos 2 \theta
Option A (12cos⁡2θ\frac{{1}}{{2}} \cos 2 \theta) is correct because using the identity cos⁡2A−sin⁡2B=cos⁡(A+B)cos⁡(A−B)\cos^2 A - \sin^2 B = \cos(A+B)\cos(A-B), the expression simplifies to 12cos⁡2θ\frac{{1}}{{2}} \cos 2 \theta.
383 Medium
383 of 394
Application +4 | -1
If tan⁡A,tan⁡B,tan⁡C\tan A, \tan B, \tan C are the roots of the cubic equation x3−7x2+11x−7=0x^3-7 x^2+11 x-7=0 then A+B+C=A+B+C=
View answer and explanation
Correct option: B
π\pi
Option B (π\pi) is correct because the sum of the roots of the cubic equation gives the tangent of the sum of the angles, which equals zero, implying the sum of the angles is π\pi.
384 Easy
384 of 394
Application +4 | -1
The value of cos⁡20∘+cos⁡80∘−3cos⁡50∘\cos 20^{\circ}+\cos 80^{\circ}-\sqrt{3} \cos 50^{\circ} is equal to -
View answer and explanation
Correct option: A
0
Option A (0) is correct because by using the sum-to-product trigonometric identity and simplifying, the expression evaluates to 0.
385 Easy
385 of 394
Application +4 | -1
The value of sin⁡(−11π3)\sin \left(\frac{-11 \pi}{3}\right) is 3m\frac{\sqrt{3}}{m}. Value of &#39;mm&#39; is
View answer and explanation
Correct option: A
2
Option A (2) is correct because given \sin x = \frac{{-26\sqrt{{6}}}}{{5}} and x in the third quadrant, calculating \cot x results in \frac{{1}}{{26\sqrt{{6}}}}.
386 Easy
386 of 394
Understanding +4 | -1
tan⁡A2\tan \frac{A}{2} is equal to
View answer and explanation
Correct option: C
±1−cos⁡A1+cos⁡A\pm \sqrt{\frac{1-\cos A}{1+\cos A}}
Option C (±1−cos⁡A1+cos⁡A\pm \sqrt{\frac{{1-\cos A}}{{1+\cos A}}}) is correct because it's a direct application of the half-angle formula for tangent.
387 Medium
387 of 394
Analyzing +4 | -1
In a △ABC,cos⁡B⋅cos⁡C+sin⁡B⋅sin⁡C⋅sin⁡2A=1\triangle A B C, \cos B \cdot \cos C+\sin B \cdot \sin C \cdot \sin ^2 A=1 Then, the triangle is
View answer and explanation
Correct option: A
right angled isosceles
Option A (right angled isosceles) is correct because the given equation implies that B=CB=C and A=π2A = \frac{\pi}{2}, making the triangle right-angled and isosceles.
388 Easy
388 of 394
Application +4 | -1
If tan⁡236∘+k(sin⁡18∘+cos⁡36∘)=5\tan ^2 36^{\circ}+k\left(\sin 18^{\circ}+\cos 36^{\circ}\right)=5, then the value of kk is
View answer and explanation
Correct option: C
4
The correct answer is C (4) because substituting the known values of sin⁡18∘\sin 18^{\circ} and cos⁡36∘\cos 36^{\circ} into the equation and solving for kk yields k=4k=4.
389 Easy
389 of 394
Application +4 | -1
If sin⁡  θ+cosec    θ=2\sin \,\,\theta + \mathrm{cosec}\;\,\,\theta = 2 then sin⁡2  θ+cosec2    θ{\sin ^2}\,\,\theta + \mathrm{cose}{\mathrm{c}^2}\;\,\,\theta is equal to
View answer and explanation
Correct option: C
2\mathrm{2}
Option C is correct because squaring the given equation and simplifying leads to sin⁡2 θ+cosec2 θ=2{\sin ^2}\,\theta + \mathrm{cose}{\mathrm{c}^2}\,\theta = 2.
390 Medium
390 of 394
Application +4 | -1
If sin⁡θ=1213(0<θ<π2)\sin \theta=\frac{12}{13}\left(0 < \theta < \frac{\pi}{2}\right) and cos⁡ϕ=−35,(π<ϕ<3π2)\cos \phi=-\frac{3}{5},\left(\pi < \phi < \frac{3 \pi}{2}\right) Then sin⁡(θ+ϕ)\sin (\theta+\phi) will be
View answer and explanation
Correct option: B
−5665\frac{-56}{65}
Option B (−5665\frac{{-56}}{{65}}) is correct because it is obtained by correctly applying the sine addition formula and considering the quadrant of ϕ\phi.
Revision notes and key takeaways

Review TRIGONOMETRY RATIOS in your textbook or class notes, then use this set to check your understanding.

Showing 361-390 of 394 questions

Continue Your Practice

📚 More Sets in This Chapter

Try different difficulty levels to master this topic

→ ENGINEERING MATHEMATICS - TRIGONOMETRY RATIOS MCQs (Easy) 218 MCQs → ENGINEERING MATHEMATICS - TRIGONOMETRY RATIOS MCQs (Hard) 19 MCQs → ENGINEERING MATHEMATICS - TRIGONOMETRY RATIOS MCQs (Medium) 157 MCQs
🎯 Next Chapters to Practice

Continue building your subject mastery

→ SEQUENCE OF SERIES 1764 MCQs → DEFINITE INTEGRATION 1443 MCQs → MATRICES 1363 MCQs → INDEFINITE INTEGRATION 1179 MCQs

Your practice

0 / 394 answered · 394 remaining · 0% accuracy

Progress is stored on this device. Sign in to save to your account.

✓ Correct · ✗ Incorrect · ○ Unanswered

Answer feedback and difficulty
Type at least 2 characters or jump directly:
🩺 NEET MCQs 🔬 JEE MCQs 🎯 JEE College Predictor Study guides 📊 Dashboard
🔓

Save your learning progress

Sign in with a free account to save your practice answers and quiz results, then return to them when you revise.

Continue with Free Account →