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ǰλãҳ >> Ϊʲôsin2x=2sinxCosx >>

Ϊʲôsin2x=2sinxCosx

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

sin(+)=sincos+cossin£ sin2x =sin(x+x) =sinxcosx+cosxsinx =2sinxcosx

ϸдֽ

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

ij˷ (sin2x)'=(2sinxcosx)'=(2sinx)'cosx+2sinx(cosx)' =2cosxcosx+2sinx(-sinx) =2(cosx^2-sinx^2) =2cos2x Ϻ󵼷 2x=t, (sin2x)'=(sint)'(2x)'=2cost=2cos2x=2(cosx^2-sinx^2)

sin2x=2sinxcosx sin4x=2sin2xcos2x Ը⣬ԼΪxǺ עⱶǹʽеĽǵıԵģ42211/2Ķ

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f(x)=sin2x+2sinx f'(x)=2cos2x+2cosx=4(cosx)^2+2cosx-2=2(2cosx-1)(cosx+1) f'(x)=0ʱf(x)ڼֵ ʱ2cosx-1=0 cosx=1/2 sinx= (3)/2 -(3)/2 sin2x=2sinx*cosx=(3)/2-(3)/2 f(x)ֵ = (3)/2 ...

¥ sinAcosA+cosAsinA = sinAcosA+sinAcosA Ȼ󲻾2sinAcosA

sin(x+x)=sinx*cosx+cosx*sinx=2sinx*cosx Ǻ͵ʽ

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