SOLUTION: If sinA+cosA=sqrt(2) then, A=45, how?

Question 926811: If sinA+cosA=sqrt(2) then, A=45, how?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
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

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