已知8cos(2a+b)+5cosb=0,求tan(a+b)*tana的值!請高手給出詳細(xì)解答!

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已知8cos(2a+b)+5cosb=0,求tan(a+b)*tana的值!解:8cos(2a+b)+5cosb=8cos[(a+b)+a]+5cos[(a+b)-a]=8[cos(a+b)*cosa-sin(a+b)sina]+5[cos(a+b)*cosa+sin(a+b)sina]=13cos(a+b)*cosa-3sin(a+b)sina=0所以13cos(a+b)*cosa=3sin(a+b)sina所以tan(a+b)*tana=13/3.