1.

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 

Answer»

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


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