Is (tan^2(θ))/(1-cos^2(θ))=sec^2(θ) ?

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

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prove (tan^2(θ))/(1-cos^2(θ))=sec^2(θ)

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Express with sin, cos

= \frac{1}{cos ^{2} ( θ )}

Rewrite using trig identities

sec^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

cos (o) = \frac{1}{sec ( o )}

sin (x) = \frac{sec ( x )}{tan ( x ) + cot ( x )}

(cot (x) + 1)^{2} = csc^{2} (x) + 2 cot (x)

sin (θ) = - cos (θ + \frac{π}{2})

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

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