Solve \sin(x)+\cos(x)=1

eozoischgc 2021-12-13 Answered
Solve sin(x)+cos(x)=1
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Expert Answer

Jeffery Autrey
Answered 2021-12-14 Author has 35 answers
sin(A+B)=sinAcosB+sinBcosA
sin2A+cos2A=1
Compare this equation to
rsin(x+a)=1
rsinxcosa+rcosxsina=1
sinx+cosx=1
cos2a+sin2a=1r2+1r2=2r2=1
r2=2r=2
And tana=1a=π4
Therefore,
2sin(x+π4)=1
sin(x+π4)=12
x+π4=π4+2kπx=2kπ
Solutions: S={2kπ,π2+2kπ},kZ
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Laura Worden
Answered 2021-12-15 Author has 45 answers
(sin(x)+cos(x))2=12
sin2(x)+2sin(x)cos(x)+cos2(x)=1
Use this identity sin2θ+cosθ=1
1+2sin(x)cos(x)=1
2sin(x)cos(x)=0
Use the identity 2sinθcosθ=sin2θ
sin2x=0
2x=0,π
x=2πn,π2+2πn
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