If $\left( {a - b} \right)\,\,\sin \,\,\left( {{\rm{\theta }} + } \right) = \left( {a + b} \right)\sin \,\,({\rm{\theta }} - \phi )\,\;{\rm{and}}\,{\rm{\;}}a\,\,\tan \,\,\frac{{\rm{\theta }}}{2}\, - \,\,b\;\tan \,\,\frac{\phi }{2} = c$, then the value of $\sin \,\,\phi $ is equal to

$\frac{{2\,ab}}{{{a^2} - \,\,{b^2} - \,\,{c^2}}}$

If $\tan A = \frac{{1 - \cos \,\,B}}{{\sin \,\,B}}$, then

$\tan \,\,2A = {\tan ^2}B + 2\,\,\tan B$

Back to MULTIPLE AND SUBMULTIPLE ANGLES

Your Progress

0 / 66 Answered

Correct

Incorrect

Accuracy

JEE • MATHEMATICS • MULTIPLE AND SUBMULTIPLE ANGLES

Multiple and submultiple angles practice · Easy

Try a question, then open “View answer” to check it. Sign in to submit answers and save progress.

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 61-66 of 66 questions

61 Easy

61 of 66

Analyzing +4 | -1

\left( {a - b} \right)\,\,\sin \,\,\left( {\mathrm{\theta } + } \right) = \left( {a + b} \right)\sin \,\,(\mathrm{\theta } - \phi )\,\;\mathrm{and}\,\mathrm{\;}a\,\,\tan \,\,\frac{\mathrm{\theta }}{2}\, - \,\,b\;\tan \,\,\frac{\phi }{2} = c

, then the value of

\sin \,\,\phi

is equal to

View answer and explanation

Correct option: B

\frac{{2\,bc}}{{{a^2} - \,\,{b^2} - \,\,{c^2}}}

Option C (

\frac{{2\,bc}}{{{{a^2} - \,{b^2} + \,{c^2}}}}

) is correct because after simplification and substitution using the given equations, it leads to the correct expression for sin(

\phi

62 Easy

62 of 66

Application +4 | -1

\tan A = \frac{{1 - \cos \,\,B}}{{\sin \,\,B}}

, then

View answer and explanation

Correct option: A

\tan \,\,2A = \tan B

Option A is correct because it correctly uses trigonometric identities to simplify the given equation and derive the relationship between

\tan 2A

and

\tan B

63 Easy

63 of 66

Application +4 | -1

The value of

\cot \,\,36^\circ \,\,\cot \,\,72^\circ

View answer and explanation

Correct option: B

\frac{1}{{\sqrt 5 }}

Option B (

\frac{1}{{\sqrt 5 }}

) is correct because by using trigonometric identities and known values of trigonometric functions for specific angles, the expression simplifies to

\frac{1}{{\sqrt 5 }}

64 Easy

64 of 66

Application +4 | -1

The value of

16\,\,\sin \,\,144^\circ \,\,\sin \,\,108^\circ \,\,\sin \,\,72^\circ \,\,\sin \,\,36^\circ

is equal to

View answer and explanation

Correct option: A

Option A (5) is correct because by using trigonometric identities and simplifying the expression

16\,\sin \,144^\circ \,\sin \,108^\circ \,\sin \,72^\circ \,\sin \,36^\circ

, we find that it is equal to 5.

65 Easy

65 of 66

Application +4 | -1

\mathrm{\;}\cos \,\,\left( {\mathrm{\theta } - \mathrm{\alpha }} \right),\,\,\cos \,\,\mathrm{\theta }\,\,\mathrm{and}\,\,\cos \,\,\left( {\mathrm{\theta } + \mathrm{\alpha }} \right)

are in HP, then

\cos \,\,\mathrm{\theta }\,\,\sec \,\,\frac{\mathrm{\alpha }}{2}

is equal to

View answer and explanation

Correct option: A

\pm \,\sqrt 2

Option A (

\pm \\,\sqrt 2

) is correct because the expression simplifies to

\pm \\,\sqrt 2

when the given cosines are in Harmonic Progression.

66 Easy

66 of 66

Application +4 | -1

\cos \,\,2\alpha = \frac{{3\cos \,\,2\beta - 1}}{{3 - \cos \,\,2\beta }}

, then

\tan \alpha

is equal to

View answer and explanation

Correct option: A

\sqrt 2 \,\,\tan \,\,\beta

Option A (

\sqrt 2 \,\,\tan \,\,\beta

) is correct because by applying componendo and dividendo,

\tan \alpha

can be expressed in terms of

\tan \beta

Revision notes and key takeaways

Review MULTIPLE AND SUBMULTIPLE ANGLES in your textbook or class notes, then use this set to check your understanding.

Showing 61-66 of 66 questions

Continue Your Practice

📚 Switch Set (EASY)

Chapter Sets

ALL 122 MCQs EASY 66 MCQs HARD 4 MCQs MEDIUM 52 MCQs

0 /66

0✓ 0✗

0% Accuracy