Question

2-(sin(x) + cos(x))² = (sinx -cosx)²
Prove this using identities ​

Answer 1

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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