Solve: sinx+cosx=sqrt(2) one the interval (-2pi<=x<=2pi) ?

Solve: sinx+cosx=sqrt(2) (-2pi<=x<=2pi)

1 Answer
Apr 9, 2018

x=pi/4, (3pi)/4, -pi/4, -(3pi)/4

Explanation:

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sinx+cosx=sqrt2

(sinx+cosx)^2=2

sin^2x+cos^2x+2sinxcosx=2

1+2sinxcosx=2

2sinxcosx=1

We have a double angle identity that give us:

sin2x=2sinxcosx

sin2x=1

2x=arcsin(1)=pi/2, (3pi)/2, -pi/2, -(3pi)/2

x=pi/4, (3pi)/4, -pi/4, -(3pi)/4