Question 926811
we are given 
sinA + cosA = sqrt(2)
square both sides of =
sin^2(A) + 2sinAcosA + cos^2(A) = 2
use identity sin^2(A)+cos^2(A) = 1
2sinAcosA +1 = 2
subtract 1 from both sides of =
2sinAcosA = 1
divide both sides of = by 2
sinAcosA = 1/2
now substitute 45 degrees for A
sin(45)*cos(45) = 1/2
0.707106781 * 0.707106781 = 1/2
0.5 = 0.5
answer checks, A = 45 degrees