Is 1-((sin^2(x)))/(1+cos(x))=cos(x) ?

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Simplify

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

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

Rewrite using trig identities

= cos (x)

We showed that the two sides could take the same form

\Rightarrow True

cot (a) = \frac{1}{tan ( a )}

cos (u) sec (u) - cos^{2} (u) = sin^{2} (u)

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

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

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

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