Simplify (1 - cos x)(1 + cos x).

Solution:

Given, the expression is (1 - cos x)(1 + cos x)

We have to simplify the expression.

By using algebraic identity,

(a + b)(a - b) = (a² + b²)

(1 - cos x)(1 + cos x) = 1 - cos²x

By using trigonometric identity,

sin²x + cos²x = 1

1 - cos²x = sin²x

(1 - cosx)(1 + cosx) = sin²x

Therefore, the simplified expression is sin²x.

Simplify (1 - cos x)(1 + cos x).

Summary:

The simplified form of the expression (1 - cosx)(1 + cosx) is sin²x.