Solve (cot \theta csc \theta ) / (1 cos \theta )

Evaluate

\frac{cot ( θ ) csc ( θ )}{1 \times cos ( θ )}

Any expression multiplied by 1 remains the same

\frac{cot ( θ ) csc ( θ )}{cos ( θ )}

Transform the expression

More Steps

\frac{\frac{c o t ( θ )}{s i n ( θ )}}{cos ( θ )}

Multiply by the reciprocal

\frac{cot ( θ )}{sin ( θ )} \times \frac{1}{cos ( θ )}

Multiply the terms

\frac{cot ( θ )}{sin ( θ ) cos ( θ )}

Use cot t = \frac{cos t}{sin t} to transform the expression

\frac{\frac{c o s ( θ )}{s i n ( θ )}}{sin ( θ ) cos ( θ )}

Multiply by the reciprocal

\frac{cos ( θ )}{sin ( θ )} \times \frac{1}{sin ( θ ) cos ( θ )}

Cancel out the common factor cos (θ)

\frac{1}{sin ( θ )} \times \frac{1}{sin ( θ )}

Multiply the terms

\frac{1}{sin ( θ ) sin ( θ )}

Multiply the terms

\frac{1}{sin ^{2} ( θ )}

Rewrite the expression

sin^{2} (θ)

Use sin^{- 2} t = 1 + tan^{2} t to transform the expression

1 + cot^{2} (θ)

Use cot^{2} t = csc^{2} t - 1 to transform the expression

1 + csc^{2} (θ) - 1

Solution

csc^{2} (θ)

Simplify the expression