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Provide solution for RD Sharma maths class 12 chapter Differential Equations exercise 21.7 question 26

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Answer: \log |\sin y|=-\sin x+C

Hint: Separate the terms of x and y and then integrate them.

Given: \frac{d y}{d x}+\frac{\cos x \sin y}{\cos y}=0

Solution: \frac{d y}{d x}+\frac{\cos x \sin y}{\cos y}=0

        \begin{aligned} &\frac{d y}{d x}=-\frac{\cos x \sin y}{\cos y} \\\\ &\frac{\cos y}{\sin y} d y=-\cos x d x \\\\ &\cot y d y=-\cos x d x \end{aligned}

          Integrating both sides

        \begin{aligned} &\int \cot y d y=-\int \cos x d x \\\\ &\log |\sin y|=-\sin x+c \end{aligned}

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