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ǰλãҳ >> Ϊʲôsin2x=2sinxCosx >>

Ϊʲôsin2x=2sinxCosx

ԴӺͽǹʽôƵ sin2x=sin(x+x) =sinxcosx+cosxsinx =2sinxcosx

Ǻ͵ҹʽ sin(x+x) = sinx cosx + cosx sinx = 2 sinx cosx

ϸдֽ

⣺fcosx=2-sin2x=2-2sinxcosxcosx=tsint=̣1-t^2ft=2-2ṭ1-t^2t=sinxfsinx=2-2sinxcosxfsinx=2-sin2x

lim[(sin2x)/x]=lim[(2sinxcosx)/x]=lim{[(2sinx)/x]•cosx}

Ȼ

sin2x=2sinxcosxsinx0Լȥsinxɵ2cosx=sinxtanx=2x=arctan2+k*(pi)sinx=0ԭʽҲx=k*(pi)ϣx=arctan2+k*(pi)k*(pi)

⣺ fcosx=2-sin2x=2-2sinxcosx cosx=t sint=̣1-t^2 ft=2-2ṭ1-t^2 t=sinx fsinx=2-2sinxcosx fsinx=2-sin2x

t=sinx+cosx=sin2x+/4 t[-2,2] sin2x=2sinxcosx=(sinx+cosx)^2-1 y=t+t*t-1/2+2 = 0.5t*t+t+1.5 t[-2,2] x=2ʱyֵ2.5+2 x=-1ʱСֵ1 yֵ[1,2.5+2]

ΪcosX- cos3X =cos(2x-x)-cos(2x+x) =cos2xcosx+sin2xsinx -(cos2xcosx-sin2xsinx) =2sin2xsinx

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