Is tan^2(θ)=(1-cos^2(θ))/(cos^2(θ)) ?

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

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

prove

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

True

Solution steps

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

Manipulating left side

tan^{2} (θ)

Express with sin, cos

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

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

tan (u) - 1 tan (u) + 1 = 1 - cot (u) 1 + cot (u)

arccsc (x) = sin (x)

cot (θ) = \frac{sin ( θ )}{cos ( θ )}

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

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