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.
Is there an error in this question or solution?
Solution Solve Sin (Tan–1 X), | X| < 1 is Equal to Concept: Properties of Inverse Trigonometric Functions.
