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

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Home Questions UBDCR69ES2

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:

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

Options:

2 sin x + log (sec x – tan x) + c

2 sin x - log (sec x – tan x)

2 sin x + log (sec x + tan x) + c

2 sin x - log (sec x + tan x) + c

Correct Answer:

2 sin x - log (sec x + tan x) + c

Explanation:

$I=\int \frac{2 \cos ^2 x-1}{\cos x} d x$

$I=\int(2 \cos x-\sec x) d x=2 \int \cos x d x-\int \sec x d x$

= 2 sin x – log| sec x + tan x| + c

Hence (4) is the correct answer.