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已知tanatanb=3,tan[(a-b)/2]=2,求cos(a+b)
人气:357 ℃ 时间:2020-06-24 22:38:27
解答
cos(a+b)=cosacosb-sinasinb
=sinasinb(1/(tanatanb)-1=sinasinb(1/3-1)=(-2/3)sinasinb
=(-1/3)[cos(a-b)-cos(a+b)].1)
cos(a-b)=2cos^2[(a-b)/2]-1 [要用到cos^2x=1/(1+tan^2x)]
=2/{1+tan^2[(a-b)/2)}-1=2/(1+4)-1=-3/5
将cos(a-b)=-3/5代入1)式可得:
-3cos(a+b)=-3/5-cos(a+b)
cos(a+b)=3/10
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