If $\frac{{\tan \,\,3A}}{{\tan A}}\,\, = k$, then $\frac{{\sin \,\,3A}}{{\sin A}}$ is equal to

$\frac{{2k}}{{k - 1}},\;\,k \in R$

$\frac{{2k}}{{k - 1}},\;\,k \in \left[ {1/3,\;\,3} \right]$

$\frac{{k - 1}}{{2k}},\,\;k \notin \left[ {1/3,\;\,3} \right]\,$

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JEE • MATHEMATICS • TRANSFORMATIONS

Transformations practice · Hard

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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.

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1 Hard

1 of 8

Analyzing +4 | -1

1 + \cos \,\,56^\circ + \cos \,\,58^\circ - \cos \,\,66^\circ = \lambda \cos \,\,28^\circ \,\,\cos \,\,29^\circ \,\,\sin \,\,33^\circ

, then

\lambda =

View answer and explanation

Correct option: C

Option C (4) is correct because by using trigonometric identities and simplification, the value of

\lambda

is found to be 4.

2 Hard

2 of 8

Analyzing +4 | -1

The value of

\sin \,\,\frac{\pi }{7}\,\,\sin \,\,\frac{{2\,\pi }}{7}\,\,\sin \,\,\frac{{3\,\pi }}{7}

, is

View answer and explanation

Correct option: B

\sqrt 7 /8

Option B (

\sqrt 7 /8

) is correct because it is the value of the product of the sines of the given angles.

3 Hard

3 of 8

Analyzing +4 | -1

The number of pairs

\left( {x,y} \right)

satisfying the equations

\sin x + \sin y = \sin \left( {x + y} \right)

and

\left| {\,x\,} \right| + \left| {\,y\,} \right| = 1

View answer and explanation

Correct option: C

Option C (6) is correct because there are six ordered pairs (x, y) that satisfy both the given trigonometric equation and the absolute value equation.

4 Hard

4 of 8

Analyzing +4 | -1

The equation

y = \sin x\sin \left( {x + 2} \right) - {\sin ^2}\left( {x + 1} \right)

represents a straight line lying in

View answer and explanation

Correct option: D

Third and fourth quadrants only

Option D (Third and fourth quadrants only) is correct because the simplified equation represents a horizontal line with a negative y-value.

5 Hard

5 of 8

Application +4 | -1

The value of

{\cot ^2}\,\,\frac{\pi }{9} + {\cot ^2}\,\,\frac{{2\,\pi }}{9} + {\cot ^2}\,\,\frac{{4\,\pi }}{9}

, is

View answer and explanation

Correct option: B

\mathrm{3}

Option B is correct because by using the identity for

\cot^2

and simplifying, we can find the value to be 3.

6 Hard

6 of 8

Analyzing +4 | -1

{\sin ^3}x\,sin\;\,3x = \sum \limits_{m = 0}^n \,{C_m}\,\cos \,\,mx

is an identity in

x

, where

{C_0},\;\,{C_1}, \ldots ,\,\,{C_n}

are constants and

{C_n} \ne 0

, then the value of

n

equals

View answer and explanation

Correct option: C

Option C (6) is correct because expanding

\sin^3 x \sin 3x

and using trigonometric identities results in a sum of cosine terms up to

\cos 6x

, making n = 6.

7 Hard

7 of 8

Analyzing +4 | -1

The value of

\mathrm{cose}{\mathrm{c}^2}\,\,\frac{\pi }{2} + \mathrm{cose}{\mathrm{c}^2}\,\,\frac{{2\pi }}{7}\,\, + \,\,\mathrm{cose}{\mathrm{c}^2}\,\,\frac{{3\pi }}{7}

View answer and explanation

Correct option: D

{2^3}

Option D (

{2^3}

) is correct because the sum of the squares of the cosecant terms simplifies to 8 using trigonometric identities and properties of roots of trigonometric equations.

8 Hard

8 of 8

Analyzing +4 | -1

\frac{{\tan \,\,3A}}{{\tan A}}\,\, = k

, then

\frac{{\sin \,\,3A}}{{\sin A}}

is equal to

View answer and explanation

Correct option: C

\frac{{2k}}{{k - 1}},\;\,k \notin \left[ {1/3,\,\;3} \right]

Option C (

\frac{{2k}}{{k - 1}},\;k \notin \left[ {1/3,\;3} \right]

) is correct because by using trigonometric identities and the given condition, we can express

\frac{{\sin \,3A}}{{\sin A}}

in terms of k, and determine the range of k.

Revision notes and key takeaways

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

Key Takeaways

✓ This set contains 8 single-correct-answer MCQs on TRANSFORMATIONS.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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