Match the followingList IList IIA- cos 3 cos-1x1- 2x -1- x2B- sin 2 sin-1x2- 4x3 - 3xC- tan 3 tan-1x3- 3x - x3-1- 3x2D- sin 2 cos-1x4- 2x2 -1

The correct option is C A 2, B 1, C 3, D 4A) cos( 3cos ^ 1 x #160;) #160; =cos( cos ^ 1 ( 4 x ^ 3 3x ) #160; #160;) #160; =4 x ^ 3 ...

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Byju's Answer

Standard XII

Mathematics

Composition of Trigonometric Functions and Inverse Trigonometric Functions

Match the fol...

Question

Match the following
List I List II
A. $c o s (3 c o s^{- 1} x)$ 1. $2 x \sqrt{1 - x^{2}}$
B. $s i n (2 s i n^{- 1} x)$ 2. $4 x^{3} - 3 x$
C. $t a n (3 t a n^{- 1} x)$ 3. $\frac{3 x - x^{3}}{1 - 3 x^{2}}$
D. $s i n (2 c o s^{- 1} x)$ 4. $2 x^{2} - 1$

A- 2, B- 1, C- 4, D- 3

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A- 2, B- 3, C- 1, D- 4

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A- 2, B- 1, C- 3, D- 4

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A- 2, B- 4, C- 3, D- 1

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Solution

The correct option is C A- 2, B- 1, C- 3, D- 4
A) $cos (3 {cos}^{- 1} x) = cos ({cos}^{- 1} (4 x^{3} - 3 x)) = 4 x^{3} - 3 x$
B) $sin (2 {sin}^{- 1} x) = sin ({sin}^{- 1} (2 x \sqrt{1 - x^{2}})) = 2 x \sqrt{1 - x^{2}}$
C) $tan (3 {tan}^{- 1} x) = tan ({tan}^{- 1} (\frac{3 x - x^{3}}{1 - 3 x^{2}})) = \frac{3 x - x^{3}}{1 - 3 x^{2}}$
D) $cos (2 {cos}^{- 1} x) = cos ({cos}^{- 1} (2 x^{2} - 1)) = 2 x^{2} - 1$

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Q. If

\frac{x^{3}}{(2 x - 1) (x + 2) (x - 3)} =

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then

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then ascending order of A, B, C is

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	List I		List II
A.	$c o s (3 c o s^{- 1} x)$	1.	$2 x \sqrt{1 - x^{2}}$
B.	$s i n (2 s i n^{- 1} x)$	2.	$4 x^{3} - 3 x$
C.	$t a n (3 t a n^{- 1} x)$	3.	$\frac{3 x - x^{3}}{1 - 3 x^{2}}$
D.	$s i n (2 c o s^{- 1} x)$	4.	$2 x^{2} - 1$

Match the followingList IList IIA.cos(3cos−1x)1.2x√1−x2B.sin(2sin−1x)2.4x3−3xC.tan(3tan−1x)3.3x−x31−3x2D.sin(2cos−1x)4.2x2−1

The correct option is C A- 2, B- 1, C- 3, D- 4A) cos(3cos−1x)=cos(cos−1(4x3−3x))=4x3−3xB) sin(2sin−1x)=sin(sin−1(2x√1−x2))=2x√1−x2C) tan(3tan−1x)=tan(tan−1(3x−x31−3x2))=3x−x31−3x2D) cos(2cos−1x)=cos(cos−1(2x2−1))=2x2−1

Match the following
List I List II
A. $c o s (3 c o s^{- 1} x)$ 1. $2 x \sqrt{1 - x^{2}}$
B. $s i n (2 s i n^{- 1} x)$ 2. $4 x^{3} - 3 x$
C. $t a n (3 t a n^{- 1} x)$ 3. $\frac{3 x - x^{3}}{1 - 3 x^{2}}$
D. $s i n (2 c o s^{- 1} x)$ 4. $2 x^{2} - 1$