Question

Simplify
(sin Θ − cos Θ)2 + (sin Θ + cos Θ)2

Answer 1

Answer in simplified form is:

(sinФ - cosФ)² + (sinФ + cosФ)² = 2

Explanation:

Given,

(sinФ - cosФ)² + (sinФ + cosФ)²

This can be simplified as:

(sin²Ф + cos²Ф - 2sinФcosФ) + (sin²Ф + cos²Ф +2sinФcosФ)

We know that : sin²Ф + cos²Ф = 1

So,

( 1 - 2sinФcosФ) + (1 + 2sinФcosФ)

or 1 + 1 -2sinФcosФ + 2sinФcosФ

or 2

Hence we got (sinФ - cosФ)² + (sinФ + cosФ)² = 2