Question

Find the derivative of
Tan ^-1 ( a sinx - b cosx ) / ( a cosx - b sinx)​

Answer 1

Answer:

y = tan^-1 [(a cos x - b sin x)/(b cos x + a sin x)]

Divide numerator & denominator by b cos x

y = tan^-1 [ (a/b - tan x)/ (1+ a/b tan x)]

Taking a/b as tan c we have

y = tan^-1 [ tan (c-x)]

y = c-x

So dy/dx = -1.