Is (1+sin(α))(1-sin(α))=cos^2(α) ?

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

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prove (1+sin(α))(1-sin(α))=cos^2(α)

prove

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

True

Solution steps

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

Manipulating left side

(1 + sin (α)) (1 - sin (α))

Expand

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

(1 + sin (α)) (1 - sin (α))

Apply Difference of Two Squares Formula:

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

a = 1, b = sin (α)

= 1^{2} - sin^{2} (α)

Apply rule

1^{a} = 1

1^{2} = 1

= 1 - sin^{2} (α)

= 1 - sin^{2} (α)

Use the Pythagorean identity:

1 = cos^{2} (α) + sin^{2} (α)

1 - sin^{2} (α) = cos^{2} (α)

= cos^{2} (α)

We showed that the two sides could take the same form

\Rightarrow True

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