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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Expand

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

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

Apply Difference of Two Squares Formula:

(a + b) (a - b) = a^{2} - b^{2}

a = 1, b = sin (x)

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

Apply rule

1^{a} = 1

1^{2} = 1

= 1 - sin^{2} (x)

= 1 - sin^{2} (x)

Use the Pythagorean identity:

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

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

= cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{cot ( x ) sec ( x )}{csc ( x )} = 1

1 + cot^{2} (θ) = csc^{2} (θ)

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

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

sin (x) cot (x) = cos (x)

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