If the equation `sin^2 x-a sin x + b = 0` has only one solution in `(0, pi)` then which of the following statements are correct?

Options

A. `a in (-oo, 1] uu [2, oo)`
B. `b in (-oo, 0] uu [1, oo)`
C. `a=1+b`
D. none of these

Answer

A, B, C

Explanation

`sin^(2)x-a sin x+b=0` has only one solution in `(0, pi)`.
`rArr sin x=1` gives one solution, and `sin x =alpha` gives other solution such that `alpha gt 1` or `alpha le 0`
`rArr (sin x-1) (sin x-alpha)=0` is the same equation as `sin^(2) x-a sin x+b=0`
`rArr 1+alpha=a` and `alpha=b`
`rArr 1+b=a` and `b gt 1` or `b le 0`
`rArr b in (-oo, 0] uu [1, oo)`
and `a in (-oo, 1] uu [2, oo)`