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Question: The value of x for which sin[cot<sup>–1</sup>(1 + x)] = cos(tan<sup>–1</sup>x) is...

The value of x for which sin[cot–1(1 + x)] = cos(tan–1x) is

A

12\frac { 1 } { 2 }

B

1

C

0

D

–12\frac { 1 } { 2 }

Answer

–12\frac { 1 } { 2 }

Explanation

Solution

sin (sin⁡−111+(1+x)2)\left( \sin ^ { - 1 } \frac { 1 } { \sqrt { 1 + ( 1 + x ) ^ { 2 } } } \right) = cos

11+(1+x)2\frac { 1 } { \sqrt { 1 + ( 1 + x ) ^ { 2 } } } =

Ž x = – 12\frac { 1 } { 2 }