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

cot (2 u) = \frac{cot ^{2} ( u ) - 1}{2 cot ( u )}

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

\frac{sin ( 2 x )}{2} = sin (x) cos (x)

sin (θ) = sin^{3} (θ) + cos^{2} (θ) sin (θ)

\frac{csc ( θ ) - cot ( θ )}{sec ( θ ) - 1} = cot (θ)

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