If sin−135+cos−1(1213)=sin−1 C,then C=

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If

s i n^{- 1} \frac{3}{5} + c o s^{- 1} (\frac{12}{13}) = s i n^{- 1} C, t h e n C =

Options:

A . 6556

B . 2465

C . 1665

D . 5665

Answer: Option D
:
D

G i v e n s i n^{- 1} C = s i n^{- 1} \frac{3}{5} + c o s^{- 1} \frac{12}{13} \Rightarrow C = s i n (s i n^{- 1} \frac{3}{5} + c o s^{- 1} \frac{12}{13}) U s i n g s i n^{(} A + B) = s i n A c o s B + c o s A s i n B \Rightarrow C = \frac{3}{5} \times \frac{12}{13} + \sqrt{1 - \frac{9}{25}} \sqrt{1 - \frac{144}{169}} \Rightarrow C = \frac{56}{65} .

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