Question

cos(x+y)=1/5,cos(x-y)=3/5则tanx.tany=?

Answer 1

cos(x+y)+cos(x-y)=2cos[(x+y+x-y)/2]cos[(x+y-x+y)/2]=2cosx*cosy=4/5

cos(x+y)-cos(x-y)=-2sin[(x+y+x-y)/2]sin[(x+y-x+y)/2]=-2sinx*siny=-2/5

cosx*cosy=2/5

sinx*siny=1/5

tanx.tany=(sinx*siny)/(cosx*cosy)=1/2