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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

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

Factor

\frac{cos ^{2} ( a ) - cos ^{2} ( a ) sin ^{2} ( a )}{sin ^{2} ( a )} : \frac{cos ^{2} ( a ) ( 1 - sin ^{2} ( a ) )}{sin ^{2} ( a )}

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

Rewrite using trig identities

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

Rewrite using trig identities

cos^{2} (a) cot^{2} (a)

We showed that the two sides could take the same form

\Rightarrow True

cos (θ) = \frac{1}{2}

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

(1 + tan^{2} (α)) (1 - sin^{2} (α)) = 1

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

tan (x) = tan (x) + 2 sin^{2} (x)

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