Skip to main content
Back to TRIGONOMETRIC EQUATIONS

Your Progress

0 / 581 Answered
0
Correct
0
Incorrect
0%
Accuracy
JEE • MATHEMATICS • TRIGONOMETRIC EQUATIONS

Trigonometric equations 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 121-150 of 581 questions

Preparing practice and saved progress…

121 Medium
121 of 581
Analyzing +4 | -1
The set of all values of λ\lambda for which the equation cos⁡22x−2sin⁡4x−2cos⁡2x=λ\cos ^2 2 x-2 \sin ^4 x-2 \cos ^2 x=\lambda has a real solution xx, is
View answer and explanation
Correct option: B
[−32,−1]\left[-\frac{3}{2},-1\right]
Option B ([−32,−1]\left[-\frac{3}{2},-1\right]) is correct because it represents the range of the given trigonometric expression after simplification and using the range of cos⁡22x\cos^2 2x.
122 Medium
122 of 581
Application +4 | -1
The values of aa for which the equation cos⁡4x−(a+2)cos⁡2x−(a+3)=0\cos ^4 x-(a+2) \cos ^2 x-(a+3)=0 possesses a solution, lies in
View answer and explanation
Correct option: A
[−3,−2][-3,-2]
Option A ([-3,-2]) is correct because by solving the quadratic equation for cos⁡2x\cos^2 x and using the fact that 0≤cos⁡2x≤10 \leq \cos^2 x \leq 1, we find that −3≤a≤−2-3 \leq a \leq -2 for the equation to possess a solution.
123 Easy
123 of 581
Application +4 | -1
If 2  cos⁡2  x+3  sin⁡  x−3=0,   0≤  x  ≤180∘2\,\,{\cos ^2}\,\,x + 3\,\,\sin \,\,x - 3 = 0,\;\,0 \le \,\,x\,\, \le 180^\circ, then the value of xx is

View answer and explanation
Correct option: A
30∘,  90∘,   150∘30^\circ ,\,\,90^\circ ,\;\,150^\circ
Option A (30∘,,90∘,;,150∘30^\circ ,\\,90^\circ ,\\;\\,150^\circ) is correct because these are the solutions to the trigonometric equation within the given range.
124 Easy
124 of 581
Application +4 | -1
If sin⁡  2x  cos⁡  2x  cos⁡  4x=λ\sin \,\,2x\,\,\cos \,\,2x\,\,\cos \,\,4x = \lambda has a solution, then λ\lambda lies in the interval
View answer and explanation
Correct option: B
[−1/4,  1/4]\left[ { - 1/4,\;1/4} \right]
Option B ([ - 1/4, 1/4 ]) is correct because the range of sin⁡8x\sin 8x is [-1, 1], which constrains the possible values of λ\lambda.
125 Easy
125 of 581
Understanding +4 | -1
The most general value of θ\theta satisfying the equations sin⁡  θ=sin⁡  α\sin \,\,\theta = \sin \,\,\alpha and cos⁡  θ=cos⁡  α\cos \,\,\theta = \cos \,\,\alpha is
View answer and explanation
Correct option: C
nπ+αn\pi + \alpha
Option A (2nπ+α2n\pi + \alpha) is correct because it represents the general solution where θ\theta and α\alpha have the same sine and cosine values, indicating they are coterminal angles.
126 Easy
126 of 581
Application +4 | -1
cos⁡23π5+cos⁡24π5\cos ^2 \frac{3 \pi}{5}+\cos ^2 \frac{4 \pi}{5} is equal to
View answer and explanation
Correct option: D
34\frac{3}{4}
Option D (34\frac{3}{4}) is correct because using the trigonometric identities and values, the expression simplifies to 34\frac{3}{4}.
127 Medium
127 of 581
Application +4 | -1
 △ABC\triangle A B C is such that sin⁡(2A+B)=12\sin (2 A+B)=\frac{1}{2}.
If A,BA, B and CC are in AP, then the values of A,BA, B and CC are
View answer and explanation
Correct option: A
π4,π3,5π12\frac{\pi}{4}, \frac{\pi}{3}, \frac{5 \pi}{12}
Option A (π4,π3,5π12\frac{\pi}{4}, \frac{\pi}{3}, \frac{5 \pi}{12}) is correct because by using the given condition and the properties of an arithmetic progression, we can find the values of A, B, and C.
128 Medium
128 of 581
Application +4 | -1
If cot⁡xcoty⁡=k\cot x \operatorname{coty}=k and x+y=π/3x+y=\pi / 3, then tan⁡x,tan⁡y\tan x, \tan y satisfy the equation
View answer and explanation
Correct option: A
kt2−3(k−1)t+1=0k t^{2}-\sqrt{3}(k-1) t+1=0
Option A is correct because it represents the quadratic equation whose roots are tan⁡x\tan x and tan⁡y\tan y, derived from the given conditions cot⁡xcot⁡y=k\cot x \cot y = k and x+y=π/3x + y = \pi/3.
129 Medium
129 of 581
Analyzing +4 | -1
If sin⁡6x=1+cos⁡43x\sin ^6 x=1+\cos ^4 3 x, then xx is equal to
View answer and explanation
Correct option: C
(2n+1)π2,n∈I(2 n+1) \frac{\pi}{2}, n \in I
Option C ((2n+1)π2,n∈I(2 n+1) \frac{\pi}{2}, n \in I) is the correct solution because it satisfies both sin⁡6x=1\sin^6 x = 1 and cos⁡43x=0\cos^4 3x = 0.
130 Medium
130 of 581
Analyzing +4 | -1
The most general values of θ\theta satisfying the equation (1+2sin⁡θ)2+(3tan⁡θ−1)2=0(1+2 \sin \theta)^2+(\sqrt{3} \tan \theta-1)^2=0 is/are given by
View answer and explanation
Correct option: C
2nπ+7π62 n \pi+\frac{7 \pi}{6}
Option C (6) is correct because solving the equation tan⁡x+cot⁡x=2csc⁡x\tan x + \cot x = 2 \csc x leads to cos⁡x=12\cos x = \frac{1}{2}, which has 6 solutions in the interval [−2π,2π][-2\pi, 2\pi].
131 Medium
131 of 581
Application +4 | -1
If the equations sin⁡θ=−12\sin \theta=-\frac{1}{2} and tan⁡θ=13\tan \theta=\frac{1}{\sqrt{3}}, then most common general value of θ\theta is
View answer and explanation
Correct option: C
2nπ+7π62 n \pi+\frac{7 \pi}{6}
Option C (2nπ+7π62 n \pi+\frac{{7 \pi}}{{6}}) is correct because it represents the general solution that satisfies both the sine and tangent equations.
132 Easy
132 of 581
Application +4 | -1
The number of roots of the equation, (81)sin⁡2x+(81)cos⁡2x=30{\left( {81} \right)^{\sin }}^{^2x} + {\left( {81} \right)^{\cos }}^{^2x} = 30 in the interval [0, π]\left[ {0,\,\pi } \right] is equal to:
View answer and explanation
Correct option: C
4
Option C (4) is correct because solving the trigonometric equation yields four solutions within the specified interval [0, π].
133 Easy
133 of 581
Application +4 | -1
The value of the expression (3sin⁡75∘−cos⁡75∘)\left(\sqrt{3} \sin 75^{\circ}-\cos 75^{\circ}\right) is
View answer and explanation
Correct option: D
2\sqrt{2}
The correct answer is 2\sqrt{2} because the expression simplifies to 2sin⁡45∘2 \sin 45^{\circ}, which equals 2\sqrt{2}.
134 Medium
134 of 581
Application +4 | -1
The most general values of xx for which 3sin⁡x−cos⁡x=min⁡λεR{2,e2,π,λ2−4λ+7}\sqrt{3} \sin x-\cos x=\min \limits_{\lambda \varepsilon {R}}\left\{2, {e}^2, \pi, \lambda^2-4 \lambda+7\right\} are given by-
View answer and explanation
Correct option: B
2nπ+2π32 {n} \pi+\frac{2 \pi}{3}
Option B (2nπ+2π32 {n} \pi+\frac{{2 \pi}}{{3}}) is correct because it represents the general solution to the trigonometric equation after simplification and solving for x.
135 Medium
135 of 581
Application +4 | -1
If tan⁡x=ba\tan x=\frac{b}{a}, then the value of acos⁡2x+bsin⁡2xa \cos 2 x+b \sin 2 x is
View answer and explanation
Correct option: A
aa
Option A (aa) is correct because by substituting tan⁡x=ba\tan x = \frac{{b}}{{a}} into the expression acos⁡2x+bsin⁡2xa \cos 2x + b \sin 2x and using trigonometric identities, the expression simplifies to aa.

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
136 Medium
136 of 581
Application +4 | -1
The general solution for α\alpha is, if 2sin⁡2α+3cos⁡α+1=02 \sin ^2 \alpha+\sqrt{3} \cos \alpha+1=0
View answer and explanation
Correct option: B
2nπ±5π62 n \pi \pm \frac{5 \pi}{6}
Option B (2nπ±5π62 n \pi \pm \frac{{5 \pi}}{{6}}) is correct because it represents the general solution derived from solving the given trigonometric equation.
137 Medium
137 of 581
Understanding +4 | -1
Which one of the following is not correct?
View answer and explanation
Correct option: C
∣sec⁡x∣<1|\sec x| < 1
The correct answer is ∣sec⁡x∣<1|\sec x| < 1 because the range of sec⁡x\sec x is (−∞,−1]∪[1,∞)(-\infty, -1] \cup [1, \infty), so its absolute value cannot be less than 1.
138 Medium
138 of 581
Analyzing +4 | -1
The graph of the function cos⁡xcos⁡(x+2)−cos⁡2(x+1)\cos x \cos (x+2)-\cos ^2(x+1) is
View answer and explanation
Correct option: D
A straight line passing through the point (π2,−sin⁡21)\left(\frac{\pi}{2},-\sin ^2 1\right) and parallel to the XX-axis
Option D (A straight line passing through the point (π2,−sin⁡21)\left(\frac{\pi}{2},-\sin ^2 1\right) and parallel to the XX-axis) is correct because the given expression simplifies to a constant value, −sin⁡21-\sin^2 1, which represents a horizontal line.
139 Easy
139 of 581
Application +4 | -1
Maximum value of the expression 2sin⁡x+4cos⁡x+32 \sin x+4 \cos x+3 is
View answer and explanation
Correct option: A
25+32 \sqrt{5}+3
Option A (25+32 \sqrt{5}+3) is correct because the maximum value of asin⁡x+bcos⁡xa \sin x + b \cos x is a2+b2\sqrt{a^2 + b^2}, and adding a constant shifts the maximum value accordingly.
140 Medium
140 of 581
Application +4 | -1
1+sin⁡  x+sin⁡2x+…1 + \sin \,\,x + {\sin ^2}x + \ldots to ∞=4+2 3\infty = 4 + 2\,\sqrt 3, if
View answer and explanation
Correct option: A
x=2π3    or,  π3x = \frac{{2\pi }}{3}\,\,\;\mathrm{or,}\,\,\frac{\pi }{3}
Option A (x=2π3    or  π3x = \frac{{2\pi }}{{3}}\,\,\;\mathrm{or}\,\,\frac{\pi }{3}) is correct because it satisfies the given infinite geometric series equation after solving for sin(x).
141 Easy
141 of 581
Application +4 | -1
Sum of the root of the equation 2sin⁡2θ+sin⁡22θ=2;0≤θ≤π/22 \sin ^2 \theta+\sin ^2 2 \theta=2 ; 0 \leq \theta \leq \pi / 2 is
View answer and explanation
Correct option: B
3π/43 \pi / 4
Option B (3π/43 \pi / 4) is correct because by simplifying the given equation and solving for θ\theta in the interval [0,π/2][0, \pi / 2], we find the roots are π/4\pi/4 and π/2\pi/2, and their sum is 3π/43\pi/4.
142 Medium
142 of 581
Analyzing +4 | -1
Let S={θ∈[−π,π]−{±π2}:sin⁡θtan⁡θ+tan⁡θ=sin⁡2θ}.S = \left\{ {\theta \in \left[ { - \pi ,\pi } \right] - \left\{ { \pm \frac{\pi }{2}} \right\}:\sin \theta \tan \theta + \tan \theta = \sin 2\theta } \right\}. If T=∑θ∈Scos⁡2θ,T = \sum\limits_{\theta \in S} {\cos 2\theta } , then T+n(S)T + n\left( S \right) is equal to:
View answer and explanation
Correct option: B
9
The correct answer is 9 because the sum of the cosines of the solutions plus the number of solutions to the trigonometric equation equals 9.
143 Medium
143 of 581
Application +4 | -1
What is sin⁡2(3π)+cos⁡2(4π)+tan⁡2(5π)\sin ^{2}(3 \pi)+\cos ^{2}(4 \pi)+\tan ^{2}(5 \pi) equal to ?
View answer and explanation
Correct option: B
1
Option B (1) is correct because it simplifies to sin⁡2(3π)+cos⁡2(4π)+tan⁡2(5π)=0+1+0=1\sin^2(3\pi) + \cos^2(4\pi) + \tan^2(5\pi) = 0 + 1 + 0 = 1.
144 Medium
144 of 581
Application +4 | -1
The solution of the trigonometric equation cos⁡2(π3cos⁡x−8π3)=1\cos ^2\left(\frac{\pi}{3} \cos x-\frac{8 \pi}{3}\right)=1 must be-
View answer and explanation
Correct option: C
2nπ2 {n} \pi
Option C (2nπ2 {n} \pi) is correct because it represents the general solution to the trigonometric equation after simplification and considering the range of cosine function.
145 Hard
145 of 581
Application +4 | -1
If ∣k∣=5|k|=5 and 0∘≤θ≤360∘0^{\circ} \leq \theta \leq 360^{\circ}, then the number of different solution of 3cos⁡θ+4sin⁡θ=k3 \cos \theta+4 \sin \theta=k is
View answer and explanation
Correct option: B
Two
Option B (Two) is correct because the equation has two solutions when ∣k∣=5|k| = 5 and 0∘≤θ≤360∘0^{\circ} \leq \theta \leq 360^{\circ}.
146 Easy
146 of 581
Application +4 | -1
Number of values of x∈[0,2π]x \in[0,2 \pi] and satisfying the equation
cos⁡xcos⁡2xcos⁡3x=1/4\cos x \cos 2 x \cos 3 x=1 / 4 is:
View answer and explanation
Correct option: B
8
The correct answer is B (8) because solving the trigonometric equation cos⁡xcos⁡2xcos⁡3x=1/4\cos x \cos 2x \cos 3x = 1/4 within the interval [0,2π][0, 2\pi] yields 8 distinct solutions.
147 Easy
147 of 581
Application +4 | -1
If 5x+1>−245 x+1>-24 and 5x−1<245 x-1 < 24, then x∈(−a,a)x \in(-a, a). The value of &#39;aa&#39; is
View answer and explanation
Correct option: A
5
Option A (5) is correct because solving the compound inequality 5x+1>−245x + 1 > -24 and 5x−1<245x - 1 < 24 results in −5<x<5-5 < x < 5, which corresponds to the interval (−5,5)(-5, 5).
148 Medium
148 of 581
Analyzing +4 | -1
If f(x)=cos⁡x(sin⁡x+sin⁡2x+sin⁡2θ),f\left( x \right) = \cos x\left( {\sin x + \sqrt {{{\sin }^2}x + {{\sin }^2}\theta } } \right), where θ\theta is a given constant, then maximum value of f(x)f(x) is
View answer and explanation
Correct option: B
1+sin⁡2θ\sqrt{1+\sin ^2 \theta}
Option B (1+sin⁡2θ\sqrt{1+\sin ^2 \theta}) is correct because by completing the square and using trigonometric identities, we can find the maximum value of f(x)f(x).
149 Easy
149 of 581
Analyzing +4 | -1
The number of values of xx lying in the interval (− π, π)\left( { - \,\mathrm{\pi },\,\mathrm{\pi }} \right) which satisfy the equation
8(1+∣cos⁡x∣+cos⁡2x+∣cos⁡3x∣+...∞)  =43{8^{(1 + |\cos x| + {{\cos }^2}x + |{{\cos }^3}x| + ...\infty )}}\,\, = {4^3}, is
View answer and explanation
Correct option: B
4
Option B (4) is correct because there are four solutions for x in the interval (-π\pi, π\pi) that satisfy the given equation.
150 Easy
150 of 581
Analyzing +4 | -1
The number of solution of tan⁡x+sec⁡x=2cos⁡x\tan x+\sec x=2 \cos x in [0,2π[0,2 \pi ) is
View answer and explanation
Correct option: B
3
The number of solutions is 3 because solving the equation leads to sin⁡x=12\sin x = \frac{1}{2} and sin⁡x=−1\sin x = -1, giving three solutions in the interval [0,2π)[0, 2\pi).
Revision notes and key takeaways

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

Showing 121-150 of 581 questions

Continue Your Practice

📚 More Sets in This Chapter

Try different difficulty levels to master this topic

→ ENGINEERING MATHEMATICS - TRIGONOMETRIC EQUATIONS MCQs (Easy) 261 MCQs → ENGINEERING MATHEMATICS - TRIGONOMETRIC EQUATIONS MCQs (Hard) 26 MCQs → ENGINEERING MATHEMATICS - TRIGONOMETRIC EQUATIONS MCQs (Medium) 294 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 / 581 answered · 581 remaining · 0% accuracy

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

✓ Correct · ✗ Incorrect · ○ Unanswered

Practice settings

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 →