The number of real solutions of the equation 2sin 3x + sin 7x – 3 = 0 which lie in the interval [–2π, 2π] is
(A) 1
(B) 2
(C) 3
(D) 4
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The number of real solutions of the equation 2sin 3x + sin 7x – 3 = 0 which lie in the interval [–2π, 2π] is
(A) 1
(B) 2
(C) 3
(D) 4
The number of real solutions of the equation 2sin 3x + sin 7x – 3 = 0 which lie in the interval [–2π, 2π] is
(A) 1
(B) 2
(C) 3
(D) 4
Correct option (B) 2
Explanation:
only possible when sin 3x = 1 & sin 7x = 1
sin 3x = 1
sin 3x = sin (4n + 1) π/2 , n ∈ I
3x = (4n + 1) π/2 ⇒ x = (4n + 1) π/6
sin 7x = sin(4m + 1) π/2, m ∈ I
x = (4m + 1) π/14
for common solution
(4n + 1) π/6 = (4m + 1) π/14
Solving these 1 = 3m – 7n
First solution is m = 5, n = 2
Second solution is m = 12, n = 5
So two solutions are possible