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Question: If sin<sup>–1</sup> x =\(\frac{\pi}{5}\) for some xÎ (–1,1), then the value of cos<sup>–1</sup> x is...

If sin–1 x =π5\frac{\pi}{5} for some xÎ (–1,1), then the value of cos–1 x is

A

3π10\frac{3\pi}{10}

B

5π10\frac{5\pi}{10}

C

7π10\frac{7\pi}{10}

D

9π10\frac{9\pi}{10}

Answer

3π10\frac{3\pi}{10}

Explanation

Solution

sin–1x = π5\frac{\pi}{5}, cos–1x = π2\frac{\pi}{2} – sin–1 x

cos–1x = π2−π5\frac{\pi}{2} - \frac{\pi}{5} = 3π10\frac{3\pi}{10}