If sinx + cosx = √2sinx, then the value of sinx - cos x is :
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Correct answer: D
Explanation
The correct answer is Option 4 i.e √2 cos x.
sinx + cosx = √2sinx
Squaring both sides
⇒ (sinx + cosx)2 = (√2sinx)2
⇒ sin2x + cos2x + 2 sinx cos x = 2sin2x
⇒ 2 sinx cosx = sin2x - cos2x
⇒ 2 sinx cosx = (sinx + cosx)(sinx - cosx)
⇒ 2 sinx cosx = (sinx - cosx) × √2sinx
⇒ √2 cosx = (sinx - cosx)
So, the value of sinx - cosx is √2 cosx