If sin^{-1} frac{3}{5} + cos^{-1} frac{12}{13 | vedclass

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(D) Given $\sin^{-1} C = \sin^{-1} \frac{3}{5} + \cos^{-1} \frac{12}{13}$.Let $\alpha = \sin^{-1} \frac{3}{5}$ and $\beta = \cos^{-1} \frac{12}{13}$.T

Vedclass · Accepted Answer

$\frac{56}{65}$

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(D) Given $\sin^{-1} C = \sin^{-1} \frac{3}{5} + \cos^{-1} \frac{12}{13}$.Let $\alpha = \sin^{-1} \frac{3}{5}$ and $\beta = \cos^{-1} \frac{12}{13}$.Then $\sin \alpha = \frac{3}{5}$,which implies $\cos \alpha = \sqrt{1 - (\frac{3}{5})^2} = \sqrt{\frac{16}{25}} = \frac{4}{5}$.And $\cos \beta = \frac{12}{13}$,which implies $\sin \beta = \sqrt{1 - (\frac{12}{13})^2} = \sqrt{\frac{25}{169}} = \frac{5}{13}$.We have $\sin^{-1} C = \alpha + \beta$,so $C = \sin(\alpha + \beta)$.Using the identity $\sin(\alpha + \beta) = \sin \alpha \cos \beta + \cos \alpha \sin \beta$:$C = (\frac{3}{5} 	imes \frac{12}{13}) + (\frac{4}{5} 	imes \frac{5}{13})$$C = \frac{36}{65} + \frac{20}{65} = \frac{56}{65}$.

If $\sin^{-1} \frac{3}{5} + \cos^{-1} \frac{12}{13} = \sin^{-1} C$,then $C =$

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