Question

(1 + sin x)(1 – sin x) = cos^2x

Answer 1

(1 + sin x)(1 – sin x) = cos^2x

1 - sin^2x = cos^2x

cos^2x = cos^2x

Explanation:

Simplify the left hand side:

(1 + sin x)(1 – sin x) = cos^2x

1 - sin^2x = cos^2x

Using the Pythagorean Identity, we can see that the two sides are equivalent if you subtract sin^2x from both sides:

sin^2x + cos^2x = 1

cos^2x = 1 - sin^2x

Lastly, write it out:

(1 + sin x)(1 – sin x) = cos^2x

1 - sin^2x = cos^2x

cos^2x = cos^2x