Question

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

Answer 1

`2sintheta=r^4-2r^2+3`
`2sintheta=(r^4-2r^2+1)+2`
`2sintheta=(r^2-1)^2+2`
LHS
`2sintheta`
`-1<=sintheta<=1`<br> `-2<=2sintheta<=2`<br> RHS
`(r^2-1)^2+2`
`0<=(r^2-1)^2<=oo`<br> `2<=(r^2-1)^2+2<=oo`<br> LHS=RHS=2
`2sintheta=2`
`sintheta=1`
`theta=pi/2,5/2pi,9/2pi`
`(r^2-1)^2+2=2`
`(r^2-1)^2=0`
`r^2=1`
`r=pm1`.