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(A) माना कि $x = \cos^{-1} \frac{1}{3} + \cos^{-1} \frac{1}{5}$ और $y = \sin^{-1} \frac{1}{3} + \sin^{-1} \frac{1}{5}$ है।हम जानते हैं कि $\cos^{-1} z

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(A) माना कि $x = \cos^{-1} \frac{1}{3} + \cos^{-1} \frac{1}{5}$ और $y = \sin^{-1} \frac{1}{3} + \sin^{-1} \frac{1}{5}$ है।हम जानते हैं कि $\cos^{-1} z = \frac{\pi}{2} - \sin^{-1} z$ होता है।अतः,$x = (\frac{\pi}{2} - \sin^{-1} \frac{1}{3}) + (\frac{\pi}{2} - \sin^{-1} \frac{1}{5}) = \pi - (\sin^{-1} \frac{1}{3} + \sin^{-1} \frac{1}{5}) = \pi - y$ है।इसलिए,$\cos(x) = \cos(\pi - y) = -\cos(y)$ होगा।अतः,$\cos(x) + \cos(y) = -\cos(y) + \cos(y) = 0$।

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

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