Find the maximum and minimum value of `y = asin^2x + b sinx.cosx + c cos^2x`

Explanation

`y=a/2[1-cos2x]+b/2[sin2x] + c/2[1+cos2x]`
`=(a/2+c/2) + (c-a)/(2) cos2x + b/2 sin2x`
Let `f(x) = (c-a)/(2)cos2x + b/2 sin2x`
`f(X)_("max") = sqrt((b/2)^(2) + ((c-a)/(2))^(2))`
`y_("max") = (a+c)/(2) + sqrt(((c-a)/2)^(2) + (b/2)^(2))`
`y_("min") =(c+a)/(2) -sqrt(((c-a)/(2))^(2)+(b/2)^(2))`
`rArr` Equation of the form
`asinx + bcosx =c`, will have at least one solution if
`sqrt(a^(2)+b^(2)) le c lt sqrt(a^(2)+b^(2))` or `|c| le sqrt(a^(2)+b^(2))`
For `|c| ge sqrt(a^(2)+b^(2))` there will be no solution.