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प्रश्न
Evaluate:
\[\int \cos^{-1} \left(\sin x \right) \text{dx}\]
उत्तर
\[\int \cos^{-1} \left(\sin x \right)\text{ dx }\]
\[= \int \cos^{-1} \left( \cos\left( \frac{\pi}{2} - x \right) \right) \text{ dx }\]
\[ = \int \left(\frac{\pi}{2} - x \right) dx\]
\[ = \frac{\pi}{2}x - \frac{1}{2} x^2 + c\]
\[\text{Hence,}\int \cos^{-1} \left(\sin x \right)\text{ dx } = \frac{\pi}{2}x - \frac{1}{2} x^2 + c\]
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