Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If x and y are the solutions of the equation 12 sin x + 5 cos x = 2y 2 -8y + 21, then the value of 
is (Given, |x |< 
)
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
5
LHS = 12sinx + 5cosx 
i.e. [-13,13] i.e.
maximum value of LHS is 13
RHS = 2 (y 2 - 4y + 4) + 13
= 2(y-2) 2 + 13
RHS 
13
Roots of the equation exist if LHS = RHS = 13.
RHS = 13 when y = 2
LHS = 13 
12sinx + 5cosx = 13
, where 
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
The number of solutions, the equation sin 4 x + cos 4 x = sinxcosx has, in [ , 5 ] is/are
Number of solutions of 2 sin(|x|) = 3 |cosx| in [- , ], is equal to
Consider the equation . If the sum of the roots is , where G.C.D (p, g) = 1, then the value of p …
If , then the number of real values of x satisfying the equation is
The number of solutions of the equation |cot x|= cot x + cosec x in [0,10 ] is/are
The sum of the roots of the equation in , then the value of 6k is