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

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

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

prove

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

True

Solution steps

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

Manipulating right side

1 - sin (a)

Multiply by

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

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

Apply Difference of Two Squares Formula:

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

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

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

Use the Pythagorean identity:

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

sin^{2} (α) sec (α) = tan^{2} (α)

1 + tan (2 x) tan (x) = sec (2 x)

\frac{4}{cos ^{2} ( x )} - 5 = 4 tan^{2} (x) - 1

(sec (x) + tan (x)) (1 - sec (x)) = cos (x)

tan (x) cos (2 x) = sin (2 x) - tan (x)

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