What is the integral of (sin(θ)-1)/(cos^2(θ)) ?

The integral of (sin(θ)-1)/(cos^2(θ)) is sec(θ)-tan(θ)+C

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integral of (sin(θ)-1)/(cos^2(θ))

\int \frac{sin ( θ ) - 1}{cos ^{2} ( θ )} d θ

sec (θ) - tan (θ) + C

Solution steps

\int \frac{sin ( θ ) - 1}{cos ^{2} ( θ )} d θ

Expand

\frac{sin ( θ ) - 1}{cos ^{2} ( θ )} : \frac{sin ( θ )}{cos ^{2} ( θ )} - \frac{1}{cos ^{2} ( θ )}

= \int \frac{sin ( θ )}{cos ^{2} ( θ )} - \frac{1}{cos ^{2} ( θ )} d θ

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{sin ( θ )}{cos ^{2} ( θ )} d θ - \int \frac{1}{cos ^{2} ( θ )} d θ

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

\int \frac{1}{cos ^{2} ( θ )} d θ = tan (θ)

= sec (θ) - tan (θ)

Add a constant to the solution

= sec (θ) - tan (θ) + C

\frac{\partial}{\partial y} (e^{- x y})

\frac{\partial}{\partial x} (y e^{\frac{x}{y}} - z)

\frac{d}{d x} (\frac{x ^{2}}{5 + 8 x})

\int \frac{1}{( x - 5 ) ( x - 3 )} d x

3 e^{- 3 t}

What is the integral of (sin(θ)-1)/(cos^2(θ)) ?
The integral of (sin(θ)-1)/(cos^2(θ)) is sec(θ)-tan(θ)+C