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