Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If α , β ( α – β ≠ 2n π, n ∈ Ι ) are different values of θ satisfying the equation 5 cos θ – 12 sin θ = 11. If the value of sin ( α + β ) = – 
, then find the value of k.
Text Solution
Verified by ExpertsThe correct answer is:
24
(24)
5 – 12 tan θ = 11 sec θ ⇒ 25 + 144 tan 2 θ – 120 tan θ = 121 + 121 tan 2 θ
23 tan 2 θ – 120 tan θ – 96 = 0 ⇒ tan α + tan β = 
⇒ tan α tan β = – 
tan ( α + β ) = 
= 
⇒ sin ( α + β ) = – 
.
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