2-(sin(x) + cos(x))² = (sinx -cosx)²
Prove this using identities
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Answer:
2–(sin x + cos x)²
= 2–(sin²x + cos²x + 2×sin x × cos x)
= 2 – (1+2×sin x × cos x)...[using sin²x+cos²x = 1]
= 2–1–2×sin x × cos x
= 1 – 2×sin x × cos x
= sin²x + cos²x– 2×sin x × cos x...[using sin²x+cos²x = 1]
= (sin x – cos x) ²
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