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

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

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

prove

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

True

Solution steps

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

Manipulating right side

1 - cos (a)

Multiply by

\frac{1 + cos ( a )}{1 + cos ( a )}

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

Apply Difference of Two Squares Formula:

a^{2} - y^{2} = (a + y) (a - y)

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

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

Use the Pythagorean identity:

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{1 - sin ( β )} + \frac{1}{1 + sin ( β )} = 2 sec^{2} (β)

cos (x + \frac{3}{2} π) = sin (x)

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

\frac{csc ( θ ) sin ( θ )}{cot ( θ )} = tan (θ)

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

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