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

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^{2} (x)

Apply Difference of Two Squares Formula:

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

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

p ro v e \frac{( cos ( x ) sec ( x ) )}{tan ( x )} = cot (x)

p ro v e (sin^{2} (x) + cos^{2} (x))^{5} = 1

p ro v e \frac{cot ^{2} ( x ) - 1}{2 cot ( x )} = cot (2 x)

p ro v e csc (θ) = \frac{sec ( θ )}{tan ( θ )}

p ro v e \frac{cos ( 2 x ) + 1}{sin ( 2 x )} = cot (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