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 )}

Rewrite using trig identities

= - cos (x)

We showed that the two sides could take the same form

\Rightarrow True

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

2 sin^{2} (θ) - 1 = 1 - 2 cos^{2} (θ)

cos (θ - π) = - cos (θ)

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

\frac{cot ^{2} ( θ )}{csc ^{2} ( θ )} = cos^{2} (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