解方程:(1)sin2x=cos3x (2)sin(2x+π/3)+sin(x-π/6)=0 (3)sin(x+π/6)
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解方程:(1)sin2x=cos3x (2)sin(2x+π/3)+sin(x-π/6)=0 (3)sin(x+π/6)+cos(x+π/6)=0
(1)sin2x-cos3x=0
sin2x-sin(π/2-3x)=0
2sin(π/4-x/2)cos(5x/2-π/4)=0
x/2-π/4=kπ或5x/2-π/4=kπ+π/2
x=2kπ+π/2或x=2kπ/5+3π/10
(2)sin(2x+π/3)=-sin(x-π/6)=sin(π/6-x)
2x+π/3=2kπ+π/6-x
x=2kπ/3-π/18
(3)tan(x+π/6)=-1=tan(-π/4)
x+π/6=kπ-π/4
x=kπ-5π/6
sin2x-sin(π/2-3x)=0
2sin(π/4-x/2)cos(5x/2-π/4)=0
x/2-π/4=kπ或5x/2-π/4=kπ+π/2
x=2kπ+π/2或x=2kπ/5+3π/10
(2)sin(2x+π/3)=-sin(x-π/6)=sin(π/6-x)
2x+π/3=2kπ+π/6-x
x=2kπ/3-π/18
(3)tan(x+π/6)=-1=tan(-π/4)
x+π/6=kπ-π/4
x=kπ-5π/6
已知sin(x+π/6)=1/3,求sin(5π/6-x)+sin^2(π/3-x)
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