Question

sinx+cosx / sinx-cosx = - tan(45+x)

Answer 1

(sin x+cos x/sinx -cos x)
divide numerator and dinominator by cos x
we get,
((tan x+1)/(tanx-1)
=-((tan45+tanx)/(1-tan 45.tanx))
=-(tan(45+x))

Answer 2

Divide the numerator and the denominator by cos x
then you will get 
Tan x +1/tan x -1
tan x + tan 45/ tan x- tan 45
multiply both numerator and the denominator by the conjugate of the denominator tan x + tan 45
on further simplification you will get the answer