tan(a+b)=5,tan(a-b)=3求tan2a,tan2b的值?
问题描述:
tan(a+b)=5,tan(a-b)=3求tan2a,tan2b的值?
答
tan(2a)=tan(a-b+a+b) =(tan(a-b)+tan(a+b))/(1-tan(a-b)tan(a+b)) =(3+5)/(1-3*5) =-4/7 tan(2b)=tan((a+b)-(a-b)) =(tan(a+b)-tan(a-b))/(1+tan(a-b)tan(a+b)) =(3-5)/(1+3*5) =-1/8