(1/2)sin2x-(根号3/2)cos2x=1/3 x∈(0,π/4)求cos2x如题

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(1/2)sin2x-(根号3/2)cos2x=1/3 x∈(0,π/4)求cos2x如题
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(1/2)sin2x-(根号3/2)cos2x=1/3 x∈(0,π/4)求cos2x如题
(1/2)sin2x-(根号3/2)cos2x=1/3 x∈(0,π/4)求cos2x
如题

(1/2)sin2x-(根号3/2)cos2x=1/3 x∈(0,π/4)求cos2x如题


(1/2)sin2x-(根号3/2)cos2x=1/3
sinπ/6sin2x-cosπ/6cos2x=1/3
cos2xcosπ/6-sin2xsinπ/6=-1/3
cos(2x+π/6)=-1/3
00<2x<π/2
π/6<2x+π/6<2π/3
∴sin(2x+π/6)>0
sin(2x+π/6)=2...

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(1/2)sin2x-(根号3/2)cos2x=1/3
sinπ/6sin2x-cosπ/6cos2x=1/3
cos2xcosπ/6-sin2xsinπ/6=-1/3
cos(2x+π/6)=-1/3
00<2x<π/2
π/6<2x+π/6<2π/3
∴sin(2x+π/6)>0
sin(2x+π/6)=2√2/3
∴cos(2x+π/6)
cos2x
=cos[(2x+π/6)-π/6]
=cos(2x+π/6)cosπ/6+sin(2x+π/6)sinπ/6
=-1/3*√3/2+2√2/3*1/2
=(-√3+2√2)/6

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