What is the integral of (tan(θ))/(sec^2(θ)) ?

The integral of (tan(θ))/(sec^2(θ)) is (sin^2(θ))/2+C

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integral of (tan(θ))/(sec^2(θ))

\int \frac{tan ( θ )}{sec ^{2} ( θ )} d θ

\frac{sin ^{2} ( θ )}{2} + C

Solution steps

\int \frac{tan ( θ )}{sec ^{2} ( θ )} d θ

Express with sin, cos

= \int cos (θ) sin (θ) d θ

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = sin (θ)

= \frac{sin ^{2} ( θ )}{2}

Add a constant to the solution

= \frac{sin ^{2} ( θ )}{2} + C

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What is the integral of (tan(θ))/(sec^2(θ)) ?
The integral of (tan(θ))/(sec^2(θ)) is (sin^2(θ))/2+C