Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:
$\int \frac{1-\tan^2 x}{1+\tan^2 x}dx$?
Options:
$\frac{\sin 2x}{2}+C$
$\frac{\cos 2x}{2}+C$
$\frac{\sin 2x}{4}+C$
$\sin 2x+C$
Correct Answer:
$\frac{\sin 2x}{2}+C$
Explanation:
$\int \frac{1-\tan^2 x}{1+\tan^2 x}dx$=$\int \frac{1-\tan^2 x}{\sec^2 x}dx=\int (\cos^2x-\sin^2x)dx=\int \cos 2xdx=\frac{sin 2x}{2}+C$