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Question: cos<sup>–1</sup>\(\left\{ \frac{1}{\sqrt{2}}\left( \cos\frac{9\pi}{10} - \sin\frac{9\pi}{10} \right)...

cos–1{12(cos⁡9π10−sin⁡9π10)}\left\{ \frac{1}{\sqrt{2}}\left( \cos\frac{9\pi}{10} - \sin\frac{9\pi}{10} \right) \right\}=

A

3π20\frac{3\pi}{20}

B

7π20\frac{7\pi}{20}

C

7π10\frac{7\pi}{10}

D

17π20\frac{17\pi}{20}

Answer

17π20\frac{17\pi}{20}

Explanation

Solution

tan (cos–1x) = sin (cot–1 12\frac{1}{2})

let cos–1 x = a and cos–1 12\frac{1}{2} = b

cos a = x Ž cot b = 12\frac{1}{2}

Ž tan a = sin b Ž 1−x2x\frac{\sqrt{1 - x^{2}}}{x} = 25\frac{2}{\sqrt{5}}

Ž 5 – 5x2 = 4x2 Ž x = ± 53\frac{\sqrt{5}}{3}