Is (1-cos(θ))(1+cos(θ))(1+cot^2(θ))=1 ?

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

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prove (1-cos(θ))(1+cos(θ))(1+cot^2(θ))=1

prove

(1 - cos (θ)) (1 + cos (θ)) (1 + cot^{2} (θ)) = 1

True

Solution steps

(1 - cos (θ)) (1 + cos (θ)) (1 + cot^{2} (θ)) = 1

Manipulating left side

(1 - cos (θ)) (1 + cos (θ)) (1 + cot^{2} (θ))

Express with sin, cos

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

Rewrite using trig identities

= 1

We showed that the two sides could take the same form

\Rightarrow True

tan^{2} (θ) - sin^{2} (θ) = sin^{2} (θ) tan^{2} (θ)

cos^{2} (2 u) - sin^{2} (2 u) = cos (4 u)

tan (u) cot (u) - cos^{2} (u) = sin^{2} (u)

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

cos (2 θ) = 1 - 2 sin^{2} (θ)

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