if sin^14A+cos^20A=x then find the smallest interval in which value of x lie

Answer 1

well, since sin^14 and cos^20 both have range [0,1], we know that x must lie in [0,2].

A little graphing shows that in fact x lies in [.006222,1]

Still haven't come up with an analysis to show that max of sin^2m(A) + cos^2n(A) = 1

or exactly what the minimum is.