Is 1+cos(θ)=(sin^2(θ))/(1-cos(θ)) ?

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

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prove 1+cos(θ)=(sin^2(θ))/(1-cos(θ))

prove

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

True

Solution steps

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

Manipulating right side

\frac{sin ^{2} ( θ )}{1 - cos ( θ )}

Rewrite using trig identities

= cos (θ) + 1

= 1 + cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

sin (2 θ) = 2 sin (2 θ) cos (2 θ)

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

\frac{cos ( 2 x )}{cos ^{2} ( x )} = 2 - sec^{2} (x)

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

sec^{2} (2 x) - tan^{2} (2 x) = 1

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