Question

已知tan(45+x)+tan(45-x)=4,且-180

Answer 1

tan(45+x)+tan(45-x)= (tan45 +tanx)/(1-tan45tanx) +(tan45-tanx)/(1+tan45tanx)

=(1+tanx)/(1-tanx) + (1-tanx)/(1+tanx)= [(1+tanx)^2+(1-tanx)^2]/[(1-tan)(1+tanx)]

= (2+2tan^2 x)/(1-tan^2x)=4

1+tan^2x=2-2tan^2x,3tan^2x=1,tan^2x =1/3,因-180