Question

Simplify (1 − cos x)(1 + cos x).

Answer 1

sin^2(x) (read as sine squared of x)

Expanding using FOIL method (distributive property) gives 1+cos(x)-cos(x)-cos^2(x), which is equal to 1-cos^2(x). This quantity is equal to sin^2(x).

Answer 2

Sin^2 x

Explanation:

● (1-cos x) (1 + cos x)

● 1^2 - cos^2 x

● 1 - cos^2 x

We khow that 1 = sin^2 x + cos^2 x

● [ sin^2 x + cos^2 x] - cos^2 x

● sin^2 x + cos^2 x - cos^2x

● sin^2 x