Is sec^2(θ)(1-cos^2(θ))=tan^2(θ) ?

The answer to whether sec^2(θ)(1-cos^2(θ))=tan^2(θ) is True

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prove sec^2(θ)(1-cos^2(θ))=tan^2(θ)

prove

sec^{2} (θ) (1 - cos^{2} (θ)) = tan^{2} (θ)

True

Solution steps

sec^{2} (θ) (1 - cos^{2} (θ)) = tan^{2} (θ)

Manipulating left side

sec^{2} (θ) (1 - cos^{2} (θ))

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

tan^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

1 - cos (x) = sin (x)

csc (x) - sin (x) = cot (x) \cdot cos (x)

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

1 - sin^{2} (- θ) = cos^{2} (θ)

Is sec^2(θ)(1-cos^2(θ))=tan^2(θ) ?
The answer to whether sec^2(θ)(1-cos^2(θ))=tan^2(θ) is True