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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.
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