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Questions  

The value of x for which sincot1(1+x)=costan1x is

a
12
b
1
c
0
d
-12

detailed solution

Correct option is D

We have, sin (cot–1 (x + 1)) = cos(tan–1 x)⇒cos⁡π2−cot−1⁡(x+1)=cos⁡tan−1⁡x⇒π2−cot−1⁡(x+1)=2nπ±tan−1⁡xPut n=0⇒π2−cot−1⁡(x+1)=±tan−1⁡x=tan−1⁡(±x)⇒π2=tan−1⁡(+x)+cot−1⁡(x+1)⇒x+1=±x⇒2x+1=0∴x=−12

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