Is cot^2(θ)(1-cos^2(θ))=cos^2(θ) ?

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

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prove cot^2(θ)(1-cos^2(θ))=cos^2(θ)

prove

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

True

Solution steps

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

Manipulating left side

cot^{2} (θ) (1 - cos^{2} (θ))

Express with sin, cos

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

Rewrite using trig identities

= cos^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

sin (\frac{π}{3} + x) - cos (\frac{π}{6} + x) = sin (x)

csc (2 x) - cot (2 x) = tan (x)

sin^{2} (x) (cot^{2} (x) + 1) = 1

tan^{2} (θ) = csc^{2} (θ) tan^{2} (θ) - 1

cos (x + \frac{π}{6}) + sin (x - \frac{π}{3}) = 0

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