What is the integral of (sec(y)tan(y)-csc(y)cot(y)) ?

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

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integral of (sec(y)tan(y)-csc(y)cot(y))

\int (sec (y) tan (y) - csc (y) cot (y)) d y

sec (y) + csc (y) + C

Solution steps

\int sec (y) tan (y) - csc (y) cot (y) d y

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 (y) tan (y) d y - \int csc (y) cot (y) d y

\int sec (y) tan (y) d y = sec (y)

\int csc (y) cot (y) d y = - csc (y)

= sec (y) - (- csc (y))

Simplify

= sec (y) + csc (y)

Add a constant to the solution

= sec (y) + csc (y) + C

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