Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If α and β are the solution of the equation a tan θ + b sec θ = c then show that tan ( α + β ) = 
Text Solution
Verified by ExpertsThe correct answer is:
A
Sol. a tan θ + b sec θ = c
⇒ (a tan θ – c) = b sec θ
squaring, we get (a tan θ – c) 2 = –b 2 sec 2 θ
⇒ a 2 tan 2 θ + c 2 – 2ac tan θ = b 2 ( 1 + tan 2 θ ) tan 2 θ (a 2 – b 2 ) –2ac tan θ + c 2 –b 2 = 0
Now α and β are solution
∴ tan α + tan β = 
and tan α tan β = 
L.H.S. tan ( α + β )= 
= 
= R.H.S.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
λ3Δ ABC and Δ DEF have sides of lengths a, b, c and d, e, f respectively (symbols are as per usual …
In a triangle ABC, ∠ A = 60 0 , a = 4 and b = 3, then c is a root of the equation
In a triangle ABC, if cos A + 2cos B + cos C = 2, then a, b, c
are in -
If in triangle ABC, r 1 = 2r 2 = 3r 3 , D is the middle point of BC. Then cos ( ∠ ADC) is equal to -
If in a triangle ABC, sin A, sin B, sin C are in A.P., then -
In triangle ABC, I is the incentre of the triangle. If ‘R’ and ‘r’ be the circumradius and inradius…