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Solve Sin (Tan–1 X), | X| < 1 is Equal to - CBSE (Science) Class 12 - Mathematics

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Question

Solve sin (tan–1 x), | x| < 1 is equal to

(A) `x/(sqrt(1-x^2))`

(B) `1/sqrt(1-x^2)`

(C) `1/sqrt(1+x^2)`

(D) `x/(sqrt(1+ x^2))`

Solution

Let tan−1 x = y. Then,  tan y = x => `sin y = x/sqrt(1+x)` 

`:. y = sin^(-1) (x/(sqrt(1+x^2))) => tan^(-1) x = sin^(-1) (x/sqrt(1+ x^2))`

`:. sin (tan^(-1) x) =  sin(sin^(-1)  x/(sqrt(1+ x^2))) = x/sqrt(1+x^2`

The correct answer is D.

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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 2: Inverse Trigonometric Functions
Q: 15 | Page no. 52
Solution Solve Sin (Tan–1 X), | X| < 1 is Equal to Concept: Properties of Inverse Trigonometric Functions.
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