Is 1-(cos^2(θ))/(1-sin(θ))=-sin(θ) ?

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

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prove 1-(cos^2(θ))/(1-sin(θ))=-sin(θ)

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= - sin (θ)

We showed that the two sides could take the same form

\Rightarrow True

sin (2 z) = 2 sin (z) cos (z)

csc^{2} (a) sec^{2} (a) = sec^{2} (a) + csc^{2} (a)

(sin^{2} (x)) (1 + cot^{2} (x)) = 1

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

\frac{1}{tan ( b )} + tan (b) = sec (b) csc (b)

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