Question

Write the following function in the simplest form:

`tan^(-1) ((cos x - sin x)/(cos x + sin x)), (-π)/4 < x < (3π)/4`

Answer 1

`tan^(-1) ((cos x - sin x)/(cos x + sin x)) = tan^(-1) ((1 - tan x)/(1 + tanx))`   ...(Dividing numerator and denominator by cos x)

= `tan^(-1) (tan (π/4 - x))`

= `π/4 - x`