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

Question

Philoid · Accepted Answer

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