Is (cot^2(θ))/(csc(θ))=csc(θ)-sin(θ) ?

The answer to whether (cot^2(θ))/(csc(θ))=csc(θ)-sin(θ) is True

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prove (cot^2(θ))/(csc(θ))=csc(θ)-sin(θ)

prove

\frac{cot ^{2} ( θ )}{csc ( θ )} = csc (θ) - sin (θ)

True

Solution steps

\frac{cot ^{2} ( θ )}{csc ( θ )} = csc (θ) - sin (θ)

Manipulating left side

\frac{cot ^{2} ( θ )}{csc ( θ )}

Express with sin, cos

= \frac{cos ^{2} ( θ )}{sin ( θ )}

Manipulating right side

csc (θ) - sin (θ)

Express with sin, cos

= \frac{1 - sin ^{2} ( θ )}{sin ( θ )}

Rewrite using trig identities

= \frac{cos ^{2} ( θ )}{sin ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

cos (4 x) = 2 cos^{2} (2 x) - 1

- cos (x) tan (x) = - sin (x)

\frac{sin ( 2 a )}{1 - cos ( 2 a )} = cot (a)

tan (x) cot (x) = sec (x) csc (x)

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

Is (cot^2(θ))/(csc(θ))=csc(θ)-sin(θ) ?
The answer to whether (cot^2(θ))/(csc(θ))=csc(θ)-sin(θ) is True