^ -1 1 5 + ^ -1 3 is equal to - Vidyadip

MCQ

$\sin ^{-1} \frac{1}{\sqrt{5}}+\cot ^{-1} 3$ is equal to

A
$\frac{\pi}{6}$
✓
$\frac{\pi}{4}$
C
$\frac{\pi}{3}$
D
$\frac{\pi}{2}$

✓

Answer

Correct option: B.

$\frac{\pi}{4}$

(B) $\sin ^{-1} \frac{1}{\sqrt{5}}+\cot ^{-1} 3=\cot ^{-1}\left(\frac{\sqrt{1-\frac{1}{5}}}{\frac{1}{\sqrt{5}}}\right)+\cot ^{-1} 3$
$\begin{array}{l}=\cot ^{-1}(2)+\cot ^{-1}(3) \\ =\cot ^{-1}\left(\frac{2 \times 3-1}{3+2}\right)\end{array}$
$=\cot ^{-1}(1)=\frac{\pi}{4}$

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