If `f(alpha)=lim_(x to 2) (sin^x alpha + cos ^x alpha)^(1/(x-2))` for `alpha in [0, pi/2]` then which of the following is correct

Options

A. `f(0)=1`
B. `f(pi/2)=1`
C. `f(alpha)=(cos alpha)^(cos^2 alpha) *(sin alpha)^(sin^2 alpha)` if `alpha in (0,pi/2)`
D. `f(alpha)=(sin alpha)^(sin^2 alpha)/(cos alpha)^(cos^2 alpha)` if `alpha in (0,pi/2)`

Answer

A: B: C