一直tanx=2 求下列各式的值(1)2/3sin2x+1/4cos2x (2)2sin2x-si
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(1)2/3sin2x+1/4cos2x

=[2/3*2sinxcosx+1/4(cos²x-sin²x)]/(sin²x+cos²x) 两边同除以cos²x

=(4/3tanx+1/4-1/4tan²x)/(tan²x+1)

∵tanx=2

∴原式=(4/3*2+1/4-1/4*2²)/(2²+1)=23/60

(2)2sin2x-sinxcosx+cos2x

=2*2sinxcosx-sinxcosx+cos²x-sin²x

=(3sinxcosx+cos²x-sin²x)/(sin²x+cos²x) 两边同除以cos²x

=(3tanx+1-tan²x)/(tan²x+1)

∵tanx=2

∴原式=(3*2+1-2²)/(2²+1)=3/5