If sin A + cos A = √2 then sin A - cos A is equal to

(a) 1

(b) 0

(c) 2

(d) none of these

Answer:

Given sin A + cos A = √2

Squaring both sides

sin2A + cos2A + 2 sin A cos A = 2

1 – cos2A + 1 – sin2 A + 2 sin A cos A = 2

2 – (cos2 A + sin2A – 2 sin A cos A) = 2

2 – (sin A – cos A)2 = 2

(sin A – cos A)2 = 0

sin A – cos A = 0

Hence option b is the answer.

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