Is 1/(1-sin^2(θ))=1+tan^2(θ) ?

The answer to whether 1/(1-sin^2(θ))=1+tan^2(θ) is True

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prove 1/(1-sin^2(θ))=1+tan^2(θ)

prove

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

True

Solution steps

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

Manipulating right side

1 + tan^{2} (θ)

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{1 - sin ^{2} ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

cos (3 x) = 4 (cos (x))^{3} - 3 cos (x)

cos (θ) = sin (\frac{π}{2} + θ)

1 - 8 sin^{2} (θ) cos^{2} (θ) = cos (4 θ)

\frac{cos ( b )}{sin ( b )} \cdot sin (b) = cos (b)

- 50 cos (4 t) + 50 = 100 sin^{2} (2 t)

Is 1/(1-sin^2(θ))=1+tan^2(θ) ?
The answer to whether 1/(1-sin^2(θ))=1+tan^2(θ) is True