Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Let a, b, c be three non-zero real numbers such that the equation 
a cos x + 2b sinx = c,
x ∈ 
, has two distinct real roots α and β with α + β = 
. Then, the value of 
is ______.
Text Solution
Verified by ExpertsThe correct answer is:
0.5
(0.5)
a cos x + 2b sin x = c x ∈ 
a 
+ 2b 
= c , where t = tan 
a(1 – t 2 ) + 4bt = c (1 + t 2 )
t 2 (c + 
a) – 4bt + c – 
a = 0
= 
tan 
= 
⇒ 
⇒ 
= 
= 
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