The value of x for which sin(cot–1(1 + x)) = cos(tan–1 x) is
We have, sin (cot–1 (x + 1)) = cos(tan–1 x)
⇒cosπ2−cot−1(x+1)=costan−1x
⇒π2−cot−1(x+1)=2nπ±tan−1x
Put n=0⇒π2−cot−1(x+1)=±tan−1x=tan−1(±x)
⇒π2=tan−1(±x)+cot−1(x+1)⇒x+1=±x⇒2x+1=0∴x=−12