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

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

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

prove

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

True

Solution steps

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

Manipulating left side

1 - sin (y)

Multiply by

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

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

Apply Difference of Two Squares Formula:

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

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

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

Use the Pythagorean identity:

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{cos ( θ ) cot ( θ )}{1 - sin ( θ )} - 1 = sin (θ)

1 = (sec (2 x))^{2} - (tan (2 x))^{2}

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

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

sin (t) cos (t) = 1

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