Is (sin^2(θ))/(1+cos(θ))=1-cos(θ) ?

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

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prove (sin^2(θ))/(1+cos(θ))=1-cos(θ)

prove

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

True

Solution steps

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

Manipulating right side

1 - cos (θ)

Multiply by

\frac{1 + cos ( θ )}{1 + cos ( θ )}

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

Apply Difference of Two Squares Formula:

θ^{2} - y^{2} = (θ + y) (θ - y)

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

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

Use the Pythagorean identity:

1 = cos^{2} (θ) + sin^{2} (θ)

1 - cos^{2} (θ) = sin^{2} (θ)

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

We showed that the two sides could take the same form

\Rightarrow True

sin^{2} (x) = 3 cos^{2} (x)

(sin (a) + cos (a))^{2} = 1 + sin (2 a)

2 cos (x) (sin (3 x) - sin (x)) = sin (4 x)

\frac{1 - sin ( θ )}{sec ( θ )} = \frac{cos ^{3} ( θ )}{1 + sin ( θ )}

2 sin (θ) = 2 sin (θ) cos (θ)

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