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

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

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

prove

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

True

Solution steps

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

Manipulating right side

1 - cos (x)

Multiply by

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

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

Apply Difference of Two Squares Formula:

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

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

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

Use the Pythagorean identity:

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

(sec^{2} (x) - 1) csc (x) = sin (x) sec^{2} (x)

\frac{1 + csc ( x )}{sec ( x )} - cot (x) = cos (x)

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

(1 - cos^{2} (x)) (1 - csc^{2} (x)) = - cos^{2} (x)

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