SOLUTION: Solve all equations for (0, 2pi) sin(x + (pi/4)) + sin(x - (pi/4)) = 1

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Question 720972: Solve all equations for (0, 2pi)
sin(x + (pi/4)) + sin(x - (pi/4)) = 1
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Solve all equations for (0, 2pi)
sin(x + (pi/4)) + sin(x - (pi/4)) = 1
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Using sin addition identities:
sin(x+π/4)=sinxcos(π/4)+cosxsin(π/4)
sin(x-π/4)=sinxcos(π/4)-cosxsin(π/4)
sinxcos(π/4)+cosxsin(π/4)+sinxcos(π/4)-cosxsin(π/4)=1
2sinxcos(π/4)=1
2sinx√2/2=1
sinx=1/√2=√2/2
x=π/4, 3π/4 (in quadrants I and II where sin>0)