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

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

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

prove

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

True

Solution steps

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

Manipulating left side

cot^{2} (θ) - cos^{2} (θ)

Express with sin, cos

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

Factor

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

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

Rewrite using trig identities

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

Rewrite using trig identities

cos^{2} (θ) cot^{2} (θ)

= cot^{2} (θ) cos^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{1 + cos ( θ )}{cos ( θ )} = sec (θ) + 1

\frac{1 + sec ( θ )}{tan ( θ ) + sin ( θ )} = csc (θ)

\frac{1}{sec ( x )} = cos (x)

sin (x) cos (x) + sin^{3} (x) sec (x) = tan (x)

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