Is tan^2(θ)=(1-cos(2θ))/(1+cos(2θ)) ?

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

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

prove

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

True

Solution steps

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

Manipulating right side

\frac{1 - cos ( 2 θ )}{1 + 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 (x + y) cos (x - y) = cos^{2} (x) - sin^{2} (x)

cos (2 θ) csc^{2} (θ) = csc^{2} (θ) - 2

cos (x) - cos (x) = 0

sec (t) - sin (t) tan (t) = cos (t)

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

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