JEE Main 2017 · 9 Apr · Shift 1 · Mathematics Q88

MathematicsSingle correct+4 / -1Question 88 of 90

A value of $x$ satisfying the equation $\sin[\cot^{-1}(1+x)]=\cos[\tan^{-1}x]$ , is :

-\dfrac12

−1

\dfrac12

Answer and worked solution

Official answer: A

$\sin(\cot^{-1}(1+x))=\dfrac1{\sqrt{1+(1+x)^2}}$ and $\cos(\tan^{-1}x)=\dfrac1{\sqrt{1+x^2}}$ . Equality needs $(1+x)^2=x^2$ , so $x=-\frac12$ .

JEE Main 2017 · 9 Apr · Shift 1, Mathematics question 88