Is 1-((sin^2(θ)))/(1+cos(θ))=cos(θ) ?

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Simplify

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

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

Rewrite using trig identities

= cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

4 sin^{2} (x) + 2 cos^{2} (x) = - 2 + 4 sin^{2} (x)

arctan (- \frac{4}{3}) = - arctan (\frac{4}{3})

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

sin (x) cos (x) = csc (x)

cos (π + x) + cos (2 π - x) = 0

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