证明:[sin(a-60)]^2+[sina]^2+[sin(a+60)]^2=3/2

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证明:[sin(a-60)]^2+[sina]^2+[sin(a+60)]^2=3/2

证明:[sin(a-60)]^2+[sina]^2+[sin(a+60)]^2=3/2
证明:[sin(a-60)]^2+[sina]^2+[sin(a+60)]^2=3/2

证明:[sin(a-60)]^2+[sina]^2+[sin(a+60)]^2=3/2
:[sin(a-60)]^2+[sina]^2+[sin(a+60)]^2
=[1/2sina-根号3/2cosa]^2+[1/2sina+根号3/2cosa]^2+sin^2a
=1/2sin^2a+3/2cos^2a+sin^2a=3/2(sin^2a+cos^2a)=3/2

[sin(a-60)]^2+[sina]^2+[sin(a+60)]^2
= [sinacos60-cosasin60)]^2+[sina]^2+[sinacos60+cosasin60)]^2
= 1/2 sin^2a + 3/2cos^2a + sin^2a = 1/2 sin^2a + 1/2cos^2a + 1
= 1/2 + 1 = 3/2

[sin(a-60)]^2+[sina]^2+[sin(a+60)]^2=[1-cos(2a-120)]/2+[sina]^2+[[1-cos(2a+120)]/2
=0.5cos2a+1+[sina]^2=0.5cos2a+1+(1-cos2a)/2=3/2