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

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

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

prove

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

True

Solution steps

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

Manipulating right side

1 - sin (x)

Multiply by

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

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

Apply Difference of Two Squares Formula:

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

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

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

Use the Pythagorean identity:

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

sin (a + b) + sin (a - b) = 2 sin (a) cos (b)

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

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

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

\frac{tan ^{2} ( x )}{sec ( x )} = sin (x) tan (x)

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