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

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(B) ધારો કે $x = \sin^{-1} \frac{3}{5}$,$y = \sin^{-1} \frac{5}{13}$,અને $z = \sin^{-1} \frac{33}{65}$ છે.$	an^{-1}$ સ્વરૂપમાં ફેરવતા:$x = 	an^{-1}

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(B) ધારો કે $x = \sin^{-1} \frac{3}{5}$,$y = \sin^{-1} \frac{5}{13}$,અને $z = \sin^{-1} \frac{33}{65}$ છે.$	an^{-1}$ સ્વરૂપમાં ફેરવતા:$x = 	an^{-1} \frac{3}{4}$,$y = 	an^{-1} \frac{5}{12}$,અને $z = 	an^{-1} \frac{33}{56}$ મળે.હવે,$	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{14/12}{33/48} ight) = 	an^{-1} \frac{56}{33}$ થાય.તેથી,પદાવલિ $\cos \left( 	an^{-1} \frac{56}{33} + 	an^{-1} \frac{33}{56} ight)$ બને છે.$	an^{-1} \frac{33}{56} = \cot^{-1} \frac{56}{33}$ હોવાથી,$\cos \left( 	an^{-1} \frac{56}{33} + \cot^{-1} \frac{56}{33} ight)$ મળે.નિત્યસમ $	an^{-1} 	heta + \cot^{-1} 	heta = \frac{\pi}{2}$ નો ઉપયોગ કરતા,$\cos \left( \frac{\pi}{2} ight) = 0$ મળે છે.

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

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