Consider the system of equations : `x sintheta-2ycostheta-az=0`, `x+2y+z=0`, `-x+y+z=0`, `theta in R`

Options

A. The given system will have infinite solutions for `a=2`
B. The number of integer values of `a` is `3` for the system to have nontrivial solutions.
C. For `a=1` there exists `theta` for which the system will have infinite solutions
D. For `a=3` there exists `theta` for which the system will have unique solutions

Answer

B, C, D

Explanation

`(b,c,d)` For the system to have nontrivial solution
`|{:(sintheta,-2costheta,-a),(-1,1,1),(1,2,1):}|=0`
i.e. `sintheta+4costheta=3a`
`implies-(sqrt(17))/(3) le a le (sqrt(17))/(3)`
`implies` a has three integer values.