if sin ( cot-1 (x + 1) ) = cos ( tan-1x ) - Maths - Inverse Trigonometric Functions

Question

if sin ( cot-1 (x + 1) ) = cos ( tan-1x )
find x i asked this question and an expert proved it wrong but this
question is absolutely correct it's 2015 board question so kindly
find x since question is correct !!! @ PRIYANKA KEDIA AND OTHER
MERITNATION EXPERTS !!!

Varun.Rawat · Accepted Answer

We have,     sincot-1x+1 = costan-1x⇒sinsin-111+x+12 = cos cos-111+x2⇒11+x+12 = 11+x2⇒1x2+2x+2 = 1x2+1⇒x2+2x+2 = x2+1⇒2x + 2 = 1⇒2x = 1 - 2⇒2x = -1⇒x = -12