Is sec(θ)(sec(θ)-cos(θ))=tan^2(θ) ?

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

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prove sec(θ)(sec(θ)-cos(θ))=tan^2(θ)

prove

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

True

Solution steps

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

Manipulating left side

sec (θ) (sec (θ) - cos (θ))

Expand

(- cos (θ) + sec (θ)) sec (θ) : - sec (θ) cos (θ) + sec^{2} (θ)

= sec^{2} (θ) - cos (θ) sec (θ)

Rewrite using trig identities

= tan^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

cos (π) = cos (- π)

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

sec^{2} (θ) - 1 = \frac{tan ( θ )}{cot ( θ )}

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

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