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

问题描述:

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