If sinx + cosx = √2, what is the value of sinx - cosx ?
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Correct answer: A
Explanation
The correct answer is option 1 i.e. 0.
sin x + cos x = √2
⇒ (sin x + cos x)2 = (√2)2
⇒ sin2x + 2sin x cos x + cos2x = 2
⇒ 1 + sin 2x = 2
⇒ sin 2x = 1
(sin x – cos x)2 = sin2x - 2sin x cos x + cos2x
=1 – sin 2x
= 1 – 1
= 0