Is (csc(θ)-sin(θ))/(cot(θ))=cos(θ) ?

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

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prove (csc(θ)-sin(θ))/(cot(θ))=cos(θ)

prove

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

True

Solution steps

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

Manipulating left side

\frac{csc ( θ ) - sin ( θ )}{cot ( θ )}

Express with sin, cos

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

Rewrite using trig identities

= cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

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

cot (x) = arctan (x)

\frac{1}{sin ( x ) cos ( x )} = \frac{2}{sin ( 2 x )}

sin (x) tan (x) = 1 + cos (x)

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