If no solution of `3siny+12sin^3x=a` lies on the line `y=3x ,` then `a in (-oo,-9)uu(9,oo)` a`a in [-9,9]` `a a in {-9,9}` `non eoft h e s e`

Options

A. `a in (-oo, -9) uu (9, oo)`
B. `a in [-9, 9]`
C. `a in {-9, 9}`
D. none of these

Answer

A

Explanation

If solution lies on the line `y=3x`, then `3 sin 3x+12 sin^(3)x=a` should have real solution.
`rArr 3(3 sin x-4 sin^(3)x)+12 sin^(3)x=a`
`rArr sinx=a/9`
Hence, for no solution, `a gt 9` or `a lt -9`.