请证明：sin^2 a+cos^2 (a+30度)

请证明：sin^2 a+cos^2 (a+30度)+sinacos(a+30度)=3/4

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左边等于sin^2a+(cosa*√3/2-sina*1/2)^2+sina*(cosa*√3/2-sina*1/2)=sin^2a+3/4cos^2a+1/4sin^2a-sina*cosa*√3/2+sina*cosa*√3/2-sin^2a*1/2=3/4(cos^2a+sin^2a)=3/4