Question

if sin x+cos x =√2 then sin x cos x=

Answer 1

sin x + cos x = √2

1/√2 sin x + 1/√2 cos x = 1

1/√2 = sin 45 = cos 45

cos 45 sin x + sin 45 cos x = sin 90

sin A cos B + cos A sin B = sin (A+B)

sin (x+45) = sin 90

x+45 = 90

x = 45°