Is (1+cot^2(θ))(1-cos^2(θ))=1 ?

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

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prove (1+cot^2(θ))(1-cos^2(θ))=1

prove

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

True

Solution steps

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

Manipulating left side

(1 + cot^{2} (θ)) (1 - cos^{2} (θ))

Express with sin, cos

= \frac{( 1 - cos ^{2} ( 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

csc (2 x) + cot (2 x) = cot (x)

cos^{2} (t) = \frac{1 + cos ( 2 t )}{2}

cos (x) csc (x) tan (x) = 1

cos (x) (csc (x) + sec (x)) = cot (x) + 1

sec (θ) cot (θ) = csc (θ)

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