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

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

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

prove

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

True

Solution steps

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

Manipulating left side

tan^{2} (θ) - sin^{2} (θ)

Express with sin, cos

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

Factor

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

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

Rewrite using trig identities

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

Rewrite using trig identities

sin^{4} (θ) sec^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

cos (- θ) = cos (θ)

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

cos (\frac{5 π}{4} - x) = - \frac{2}{2} (cos (x) + sin (x))

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

5 cos^{2} (θ) + 3 sin^{2} (θ) = 3 + 2 cos^{2} (θ)

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