Question:
Mark the tick against the correct answer in the following:
If $x \neq 0$ then $\cos \left(\tan ^{-1} x+\cot ^{-1} x\right)=?$
A. $-1$
B. 1
C. 0
D. none of these
Solution:
Given: $x \neq 0$
To Find: The value of $\cos \left(\tan ^{-1} x+\cot ^{-1} x\right)$
Now, let $x=\cos \left(\tan ^{-1} x+\cot ^{-1} x\right)$
$\Rightarrow x=\cos \left(\frac{\pi}{2}\right)\left(\because \tan ^{-1} \theta+\cot ^{-1} \theta=\frac{\pi}{2}\right)$
$\Rightarrow x=0\left(\because \cos \left(\frac{\pi}{2}\right)=0\right)$