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Question: If \(\cos ec^{- 1}x = 2\cos^{- 1}7 + \cos^{- 1}\left( \frac{3}{5} \right)\) then the value of \(x\)i...

If cos⁡ec−1x=2cos⁡−17+cos⁡−1(35)\cos ec^{- 1}x = 2\cos^{- 1}7 + \cos^{- 1}\left( \frac{3}{5} \right) then the value of xxis

A

44/117

B

125/117

C

24/7

D

5/3

Answer

125/117

Explanation

Solution

2cot⁡−17+cos⁡−1(35)=cot⁡−172−12 x 7+cot⁡−1342\cot^{- 1}7 + \cos^{- 1}\left( \frac{3}{5} \right) = \cot^{- 1}\frac{7^{2} - 1}{2\text{ x 7}} + \cot^{- 1}\frac{3}{4}

= cot⁡−1247+cot⁡−134\cot^{- 1}\frac{24}{7} + \cot^{- 1}\frac{3}{4}

= cot⁡−1247 x 34−1247+34\cot^{- 1}\frac{\frac{24}{7}\text{ x }\frac{3}{4} - 1}{\frac{24}{7} + \frac{3}{4}}

=cot⁡−144117= \cot^{- 1}\frac{44}{117}

=cos⁡ec−1125117= \cos ec^{- 1}\frac{125}{117}