What is (cos^2(θ)-1)/(sin(x)) ?

The solution to (cos^2(θ)-1)/(sin(x)) is -sin^2(θ)csc(x)

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simplify (cos^2(θ)-1)/(sin(x))

simplify

\frac{cos ^{2} ( θ ) - 1}{sin ( x )}

- sin^{2} (θ) csc (x)

Solution steps

\frac{cos ^{2} ( θ ) - 1}{sin ( x )}

Simplify

cos^{2} (θ) - 1 : - sin^{2} (θ)

= \frac{- sin ^{2} ( θ )}{sin ( x )}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{sin ^{2} ( θ )}{sin ( x )}

Use the basic trigonometric identity:

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

= - sin^{2} (θ) csc (x)

\frac{1}{cos ( π x )}

3 sin (2 x - \frac{π}{4}) + 2

1 - cot (\frac{π}{2} - x)

\frac{cos ^{2} ( x )}{sin ( - 1 )}

sin (\frac{19 π}{2} + x)

What is (cos^2(θ)-1)/(sin(x)) ?
The solution to (cos^2(θ)-1)/(sin(x)) is -sin^2(θ)csc(x)