Is cot^2(x)-cot^2(x)cos^2(x)=cos^2(x) ?

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

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prove cot^2(x)-cot^2(x)cos^2(x)=cos^2(x)

prove

cot^{2} (x) - cot^{2} (x) cos^{2} (x) = cos^{2} (x)

True

Solution steps

cot^{2} (x) - cot^{2} (x) cos^{2} (x) = cos^{2} (x)

Manipulating left side

cot^{2} (x) - cot^{2} (x) cos^{2} (x)

Express with sin, cos

= \frac{cos ^{2} ( x ) - cos ^{4} ( x )}{sin ^{2} ( x )}

Rewrite using trig identities

= cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

tan (x - π) = tan (x)

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

(1 - sin^{2} (x)) sec^{2} (x) = 1

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

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

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