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

Solution:

Given,

(1 - sinx)(1 + sinx)

We have to simplify the expression.

By using algebraic identity,

(a + b)(a - b) = (a² + b²)

We get

(1 - sinx)(1 + sinx) = 1 - sin²x

By using trigonometric identity,

sin²x + cos²x = 1

We get

1 - sin²x = cos²x

(1 - sinx)(1 + sinx) = cos²x

Therefore, the simplified expression is cos²x.

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

Summary:

The simplified form of the expression (1 - sinx)(1 + sinx) is cos²x.