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show that (Sin x+cos x)^2 +( sinx -cos x)^2=2

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Regalmocha17idn

Proving that: (sin x + cos x)² + (sin x - cos x)² = 2

Work.

(sin x + cos x)² + (sin x - cos x)² = 2  

Distribute.

(sin²x + 2 sin x cos x + cos²x ) + (sin²x - 2 sin x cos x + cos²x) = 2

Combine like terms.

sin²x + cos²x + sin²x + cos²x = 2

Pythagorean identity where sin²x + cos²x = 1.

1 + 1 = 2

2 = 2

Thus, (sin x + cos x)² + (sin x - cos x)² = 2

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