[ ^ -1 1 3 + ^ -1 1 2 ]= - Vidyadip

MCQ

$\cos \left[\tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{2}\right]=$

✓
$\frac{1}{\sqrt{2}}$
B
$\frac{\sqrt{3}}{2}$
C
$\frac{1}{2}$
D
$\frac{\pi}{4}$

✓

Answer

Correct option: A.

$\frac{1}{\sqrt{2}}$

(A) $\cos \left[\tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{2}\right]=\cos \left[\tan ^{-1}\left(\frac{\frac{1}{3}+\frac{1}{2}}{1-\frac{1}{3} \times \frac{1}{2}}\right)\right]$
$\begin{array}{l}=\cos \left\{\tan ^{-1}(1)\right\} \\ =\cos \frac{\pi}{4}=\frac{1}{\sqrt{2}}\end{array}$

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