What is the integral of (cos(t))/(sin^2(t)) ?

The integral of (cos(t))/(sin^2(t)) is -csc(t)+C

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integral of (cos(t))/(sin^2(t))

\int \frac{cos ( t )}{sin ^{2} ( t )} d t

- csc (t) + C

Solution steps

\int \frac{cos ( t )}{sin ^{2} ( t )} d t

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = sin (t)

= - \frac{1}{sin ( t )}

Use the basic trigonometric identity:

\frac{1}{sin ( x )} = csc (x)

= - csc (t)

Add a constant to the solution

= - csc (t) + C

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What is the integral of (cos(t))/(sin^2(t)) ?
The integral of (cos(t))/(sin^2(t)) is -csc(t)+C