If α And β are two solutions of the equation Atanx + Bsecx = c, then find the values of sin(α + β).

Given equation Atanx + Bsecx = c

c – Atanx = Bsecx

Squaring onBoth sides,

(c – Atanx)2 = (Bsecx)2

c2 + A2tan2 x – 2actan x =B2sec2 x

c2 +A2 tan2 x – 2ac tan x = B2(1 + tan2 x)

(a2 –B2) tan2 x – 2ac tan x +(c2 –B2) = 0

There are two solutions tan α And tan β in this quadratic.

We know that