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

sin (2 x) = 2 \cdot sin (x) \cdot cos (x)

3 tan (A) = \frac{1}{tan ( B )}

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

csc (2 y) = csc (y) 7

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

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