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

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

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

prove

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

True

Solution steps

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

\frac{1}{1 - cos ( x )} + \frac{1}{1 + cos ( x )} = csc (x^{2})

\frac{sin ( 2 x )}{2} = cos (x) sin (x)

\frac{1 + tan ^{2} ( x )}{cot ^{2} ( x ) + 1} = tan^{2} (x)

7 sec (y) cos (y) = 7

(1 + sin (a)) (1 - sin (a)) = \frac{1}{sec ^{2} ( a )}

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