Problem

20. \( \frac{\sec x \sin x+\cos \left(\frac{\pi}{2}-x\right)}{1+\sec x} \)

Answer

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Answer

\( \sin x \)

Steps

Step 1 ：\( \frac{\sec x \sin x+\cos \left(\frac{\pi}{2}-x\right)}{1+\sec x} \)

Step 2 ：\( \frac{\frac{1}{\cos x} \sin x + \cos \left(\frac{\pi}{2} - x\right)}{1 + \frac{1}{\cos x}} \)

Step 3 ：\( \frac{\frac{\sin x}{\cos x} + \sin x}{\frac{\cos x + 1}{\cos x}} \)

Step 4 ：\( \frac{\sin x (1 + \cos x)}{1 + \cos x} \)

Step 5 ：\( \sin x \)

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