What is the integral of sec(θ)tan(θ)+csc(θ)cot(θ) ?

The integral of sec(θ)tan(θ)+csc(θ)cot(θ) is sec(θ)-csc(θ)+C

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integral of sec(θ)tan(θ)+csc(θ)cot(θ)

\int sec (θ) tan (θ) + csc (θ) cot (θ) d θ

sec (θ) - csc (θ) + C

Solution steps

\int sec (θ) tan (θ) + csc (θ) cot (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 sec (θ) tan (θ) d θ + \int csc (θ) cot (θ) d θ

\int sec (θ) tan (θ) d θ = sec (θ)

\int csc (θ) cot (θ) d θ = - csc (θ)

= sec (θ) - csc (θ)

Add a constant to the solution

= sec (θ) - csc (θ) + C

What is the integral of sec(θ)tan(θ)+csc(θ)cot(θ) ?
The integral of sec(θ)tan(θ)+csc(θ)cot(θ) is sec(θ)-csc(θ)+C