$\int \frac{\cos 2 x}{\cos x+\sin x} d x

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:

$\int \frac{\cos 2 x}{\cos x+\sin x} d x$ is equal to

Options:

sin x – cos x + c

–sin x + cos x + c

sin x + cos x + c

none of these

Correct Answer:

sin x + cos x + c

Explanation:

$\int \frac{\cos 2 x}{\cos x+\sin x} d x=\int \frac{(\cos x+\sin x)(\cos x-\sin x)}{\cos x+\sin x} d x=\sin x+\cos x+c$

Hence (3) is the correct answer.