If `theta in [0,5pi]a n dr in R` such that `2sintheta=r^4-2r^2+3` then the maximum number of values of the pair `(r ,theta)` is____

Answer

6

Explanation

`2 sin theta=r^(4) - 2 r^(2) +3`
`rArr 2 sin theta=(r^(2)-1)^(2) +2`
This is possible only when `sin theta=1` and `r^(2) =1` or `r= pm 1`. So, `theta=pi//2, 5 pi//2, 9 pi//2`
`:.` Number of values of the pair `(r, theta)=6`