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

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

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

prove

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

True

Solution steps

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

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

cot (x) tan (x) = (sec (x)) (csc (x))

csc^{2} (t) = cot^{2} (t) + 1

2 tan (x) = 1

\frac{1}{csc ( x ) - 1} = 1 - sin (x)

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