If cos-1513+cos-135=cos-1x then x=

cos-1513=A , cos-135=B cosA=513 , cos B=35 x=cos(A+B)=513×35-1213×45=-3365

If cos-1513+cos-135=cos-1x then x=

cos-1513=A , cos-135=B cosA=513 , cos B=35 x=cos(A+B)=513×35-1213×45=-3365

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If $\cos^{- 1} (\frac{5}{13}) + \cos^{- 1} (\frac{3}{5}) = \cos^{- 1} x$ then $x =$

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$\frac{3}{65}$

$\frac{- 36}{65}$

$\frac{- 33}{65}$

$- 1$

answer is C.

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Detailed Solution

$\cos^{- 1} \frac{5}{13} = A, \cos^{- 1} (\frac{3}{5}) = B \cos A = \frac{5}{13}, \cos B = \frac{3}{5}$

$x = \cos (A + B) = \frac{5}{13} \times \frac{3}{5} - \frac{12}{13} \times \frac{4}{5} = \frac{- 33}{65}$

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If $\cos^{- 1} (\frac{5}{13}) + \cos^{- 1} (\frac{3}{5}) = \cos^{- 1} x$ then $x =$