怎么证明sin^2(a)+cos^2(a+30)+sinacos(a+30)=3⼀4

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2024-12-31 15:39:50
推荐回答(1个)
回答1:

左边=(1-cos2α)/2+(1+cos(2α+60°))/2+sinαcos(α+30°)
=1+1/2[cos(2α+60°)-cos2α]+1/2[sin(2α+30°)-1/2]
=3/4-1/2cos2α+1/2[sin(2α+30°)-sin(2α-30°)]
=3/4-1/2cos2α+1/2[2cos2αsin30°]
=3/4
=右边