If sin x cos x squareroot 2 sinx A pi then the number 0 S

If sin x + cos x = squareroot 2 sin(x + A pi), then the number 0

Solution

sin x + cos x = sqrt 2 sin ( x + A pi )

we can write , sin x + cos x = sqrt 2 * 1/ sqrt 2 ( sin x + cos x)

distributing 1/ sqrt 2

= sqrt 2 ( sin x / sqrt 2 + cos x / sqrt 2 )

1/ sqrt 2 = sin pi/4 , cos pi/4

= sqrt 2 ( sin x cos pi/4 + cos x sin pi/4 )

applying sin ( a+ b ) formula

so,

sin x + cos x = sqrt 2 sin ( x + 1/4 * pi )

hence , A = 1/4