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

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

True

Solution steps

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

Manipulating left side

cos^{2} (x)

Use the Pythagorean identity:

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

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

= 1 - sin^{2} (x)

Factor

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

= (1 + sin (x)) (1 - sin (x))

We showed that the two sides could take the same form

\Rightarrow True

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

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

csc (x) \cdot cos^{2} (x) + sin (x) = csc (x)

cos (2 u) = 2 cos^{2} (u) - 1

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