Question

tan inverse into cos x minus sin x by cos x + sin x

Answer 1

Given tan^-1 (cos x-sin x/cos x + sinx) can be written as

         = tan^-1(cosx/cosx - sinx/cosx / cosx/cosx + sinx/cosx)

        = tan^-1(1-tanx/1+tanx)

        = tan^-1  tan(pi/4 - x)

        = pi/4 - x.


Hope this helps!