The number of real solutions of the equation 2 sin 3x + sin 7x - 3 = 0 which lie in the interval `[-2pi , 2pi]` is

Options

A. 1
B. 2
C. 3
D. 4

Answer

B

Explanation

only possible when sin 3x = 1 & sin 7x = 1
sin 3x = 1
sin3x = sin(4n+ 1) `(pi)/(2) n in I`
` 3 x = (4n+1)(pi)/(2)implies x=(4n+1)(pi)/(6)`
`sin 7x= sin(4m+1)(pi)/(2), m in I`
`x=(4m+1)(pi)/(14)`
for common solution
`(4n+1)(pi)/(6)=(4m+1)(pi)/(14)`
Solving these `1=3m-7n`
First solution ios m=5,n=2
Second solution is m=12,n=5
So two solutions are possible