sin (tan–1 x), |x|

Question

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

KollegeApply · Accepted Answer

sin (tan–1 x), |x| < 1 is equal to `bbunderline (x/(sqrt(1+ x^2)))`. Explanation: Let tan–1 x = y. Then, tan y = x $\Rightarrow$ sin y = x/sqrt(1 + x^2) $\therefore$ y = sin^-1 (x/sqrt(1 + x^2)) $\Rightarrow$ `tan^-1x = sin^-1 (x/sqrt(1 + x^2)) $\therefore$ sin (tan^-1x) = sin (sin^-1 x/sqrt(1 + x^2)) = x/sqrt(1 + x^2)`

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