Mark the tick against the correct answer in the following:

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 $x=\cos \left(\tan ^{-1} x+\cot ^{-1} x\right)$

$\Rightarrow x=\cos \left(\frac{\pi}{2}\right)\left(\because \tan ^{-1} \theta+\cot ^{-1} \theta=\frac{\pi}{2}\right)$

$\Rightarrow x=0\left(\because \cos \left(\frac{\pi}{2}\right)=0\right)$

 

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