Evaluate integral of (sin(2x))/(cos(x)) with respect to x

$\int \frac{\sin (2 x)}{\cos (x)} d x$

Apply the sine double–angle identity.

$\int \frac{2 \sin (x) \cos (x)}{\cos (x)} d x$

Cancel the common factor of $\cos (x)$ .

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Cancel the common factor.

$\int \frac{2 \sin (x) \cos (x)}{\cos (x)} d x$

Divide $2 \sin (x)$ by $1$ .

$\int 2 \sin (x) d x$

Since $2$ is constant with respect to $x$ , move $2$ out of the integral.

$2 \int \sin (x) d x$

The integral of $\sin (x)$ with respect to $x$ is $- \cos (x)$ .

$2 (- \cos (x) + C)$

Simplify the answer.

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Simplify.

$2 (- \cos (x)) + C$

Multiply $- 1$ by $2$ .

$- 2 \cos (x) + C$

Evaluate integral of (sin(2x))/(cos(x)) with respect to x

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