cos left(sin ^{-1} frac{3}{5}+sin ^{-1} frac{ | vedclass

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(B) Let $x = \sin^{-1} \frac{3}{5}$,$y = \sin^{-1} \frac{5}{13}$,and $z = \sin^{-1} \frac{33}{65}$.Converting to $	an^{-1}$ form:$x = 	an^{-1} \frac

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(B) Let $x = \sin^{-1} \frac{3}{5}$,$y = \sin^{-1} \frac{5}{13}$,and $z = \sin^{-1} \frac{33}{65}$.Converting to $	an^{-1}$ form:$x = 	an^{-1} \frac{3}{4}$,$y = 	an^{-1} \frac{5}{12}$,and $z = 	an^{-1} \frac{33}{56}$.Now,calculate $	an^{-1} \frac{3}{4} + 	an^{-1} \frac{5}{12} = 	an^{-1} \left( \frac{\frac{3}{4} + \frac{5}{12}}{1 - \frac{3}{4} \cdot \frac{5}{12}} ight) = 	an^{-1} \left( \frac{\frac{9+5}{12}}{1 - \frac{15}{48}} ight) = 	an^{-1} \left( \frac{14/12}{33/48} ight) = 	an^{-1} \left( \frac{14}{12} \cdot \frac{48}{33} ight) = 	an^{-1} \frac{56}{33}$.Then,the expression becomes $\cos \left( 	an^{-1} \frac{56}{33} + 	an^{-1} \frac{33}{56} ight)$.Since $	an^{-1} \frac{33}{56} = \cot^{-1} \frac{56}{33}$,we have $\cos \left( 	an^{-1} \frac{56}{33} + \cot^{-1} \frac{56}{33} ight)$.Using the identity $	an^{-1} 	heta + \cot^{-1} 	heta = \frac{\pi}{2}$,we get $\cos \left( \frac{\pi}{2} ight) = 0$.

$\cos \left(\sin ^{-1} \frac{3}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{33}{65}\right) = . . . . .$

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