Is tan^4(θ)=tan^2(θ)sec^2(θ)-tan^2(θ) ?

The answer to whether tan^4(θ)=tan^2(θ)sec^2(θ)-tan^2(θ) is True

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prove tan^4(θ)=tan^2(θ)sec^2(θ)-tan^2(θ)

prove

tan^{4} (θ) = tan^{2} (θ) sec^{2} (θ) - tan^{2} (θ)

True

Solution steps

tan^{4} (θ) = tan^{2} (θ) sec^{2} (θ) - tan^{2} (θ)

Manipulating right side

tan^{2} (θ) sec^{2} (θ) - tan^{2} (θ)

Rewrite using trig identities

= tan^{4} (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

sin (2 θ) = 2 sin (2 θ) cos (2 θ)

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

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

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

Is tan^4(θ)=tan^2(θ)sec^2(θ)-tan^2(θ) ?
The answer to whether tan^4(θ)=tan^2(θ)sec^2(θ)-tan^2(θ) is True