Is cos^2(θ)=(1+sin(θ))(1-sin(θ)) ?

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

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prove cos^2(θ)=(1+sin(θ))(1-sin(θ))

prove

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

True

Solution steps

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

Manipulating left side

cos^{2} (θ)

Use the Pythagorean identity:

cos^{2} (θ) + sin^{2} (θ) = 1

cos^{2} (θ) = 1 - sin^{2} (θ)

= 1 - sin^{2} (θ)

Factor

1 - sin^{2} (θ) : (1 + sin (θ)) (1 - sin (θ))

= (1 + sin (θ)) (1 - sin (θ))

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

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

cos (θ) - sin (θ) sin (2 θ) = cos (θ) cos (2 θ)

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