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Question

Question: \(\sin^{- 1}\frac{1}{\sqrt{5}} + \cot^{- 1}3\) is equal to...

sin⁡−115+cot⁡−13\sin^{- 1}\frac{1}{\sqrt{5}} + \cot^{- 1}3 is equal to

A

π6\frac{\pi}{6}

B

π4\frac{\pi}{4}

C

π3\frac{\pi}{3}

D

π2\frac{\pi}{2}

Answer

π4\frac{\pi}{4}

Explanation

Solution

sin⁡−115+cot⁡−13=cot⁡−1(1−1515)+cot⁡−13\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= cot⁡−1(2)+cot⁡−1(3)=cot⁡−1(2×3−13+2)=cot⁡−1(1)=π4\cot^{- 1}(2) + \cot^{- 1}(3) = \cot^{- 1}\left( \frac{2 \times 3 - 1}{3 + 2} \right) = \cot^{- 1}(1) = \frac{\pi}{4}