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

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

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

prove

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

True

Solution steps

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

Manipulating left 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

sec (θ) tan (θ) = sin (θ) sec^{2} (θ)

(sec (u) - tan (u)) (csc (u) + 1) = cot (u)

cot (2 θ) = \frac{csc ^{2} ( θ ) - 2}{2 cot ( θ )}

tan (θ + \frac{π}{4}) = \frac{1 + tan ( θ )}{1 - tan ( θ )}

tan (θ) = \frac{1}{cot ( θ )}

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