What is the integral of 1/(cos(y)cot(y)) ?

The integral of 1/(cos(y)cot(y)) is sec(y)+C

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integral of 1/(cos(y)cot(y))

\int \frac{1}{cos ( y ) cot ( y )} d y

sec (y) + C

Solution steps

\int \frac{1}{cos ( y ) cot ( y )} d y

Rewrite using trig identities

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

Apply u-substitution

: \int 1 d u

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

u = sec (y)

= 1 \cdot sec (y)

Simplify

= sec (y)

Add a constant to the solution

= sec (y) + C

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What is the integral of 1/(cos(y)cot(y)) ?
The integral of 1/(cos(y)cot(y)) is sec(y)+C