已知cosa=,cos(a-b)=,且0<b<a<. (1)求tan2a的值; (2)求

已知cosa=,cos(a-b)=,且0<b<a<.

(1)求tan2a的值; (2)求角b的值.

答案

(Ⅰ)  -  (Ⅱ) b=


解析:

(1)由cosa=,0<a<,得sina=.所以tana==4

tan2a==-.

(2)由0<b<a<得0<a-b<,又cos(a-b)=,所以sin(a-b)=.cosb=cos[a-(a-b)]=cosacos(a-b)+sinasin(a-b)=×+×=,所以b=.

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