Question

sinx+siny=1/3 ,cosx+cosy=1/2,求tan(x+y)的值．

Answer 1

由和差化积公式:

sinx+siny=2sin[(x+y)/2]cos[(x-y)/2]=1/3

cosx+cosy=2cos[(x+y)/2]cos[(x-y)/2]=1/2

两式相除：

tg[(x+y)/2]=2/3

所以

tg(x+y)由2倍角公式即可求得.

tan(x+y)=2tan[(x+y)/2]/{1-tan^2[(x+y)/2]=}

=2*2/3/(1-(2/3)^2)=12/5