Is (1-cos^2(θ))(csc^2(θ))=1 ?

The answer to whether (1-cos^2(θ))(csc^2(θ))=1 is True

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prove (1-cos^2(θ))(csc^2(θ))=1

prove

(1 - cos^{2} (θ)) (csc^{2} (θ)) = 1

True

Solution steps

(1 - cos^{2} (θ)) csc^{2} (θ) = 1

Manipulating left side

(1 - cos^{2} (θ)) csc^{2} (θ)

Express with sin, cos

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

Rewrite using trig identities

= 1

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{arctan ( x )} = arccot (x)

\frac{1}{sin ( θ ) cos ( θ )} - tan (θ) = cot (θ)

(- sin (x)) (3 cos (x)) = - 3 sin (x) cos (x)

cot (θ) \cdot sec (θ) = \frac{1}{cos ( θ )}

sin (x) sin (y) = 2 sin (\frac{x + y}{2}) cos (\frac{x - y}{2})

Is (1-cos^2(θ))(csc^2(θ))=1 ?
The answer to whether (1-cos^2(θ))(csc^2(θ))=1 is True