What is the integral of (sin(2θ))/(cos(θ)) ?

The integral of (sin(2θ))/(cos(θ)) is -2cos(θ)+C

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integral of (sin(2θ))/(cos(θ))

\int \frac{sin ( 2 θ )}{cos ( θ )} d θ

- 2 cos (θ) + C

Solution steps

\int \frac{sin ( 2 θ )}{cos ( θ )} d θ

Rewrite using trig identities

= \int 2 sin (θ) d θ

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int sin (θ) d θ

Use the common integral:

\int sin (θ) d θ = - cos (θ)

= 2 (- cos (θ))

Simplify

= - 2 cos (θ)

Add a constant to the solution

= - 2 cos (θ) + C

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What is the integral of (sin(2θ))/(cos(θ)) ?
The integral of (sin(2θ))/(cos(θ)) is -2cos(θ)+C