SOLUTION: sin(theta) + cos(theta) = sqrt(2) Solve on the interval of [0,2pi)

Question 921832: sin(theta) + cos(theta) = sqrt(2) Solve on the interval of [0,2pi)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
sin(theta) + cos(theta) = sqrt(2) Solve on the interval of [0,2pi)
sinx+cosx=√2
square both sides:
sin^2x+2sinxcosx+cos^2x=2
sin^x+cos^2x=1
2sinxcosx=sin2x
sin^2x+2sinxcosx+cos^2x=2
sin2x+1=2
sin2x=1
2x=π/2
x=π/4

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