Range; a proof

What is the proof to this function range:
f(x)=Sin^2k x + Cos^2k x
R=[1/2^(k-1) , 1]

Use .



I'll work on your problem

I think this is the right range:
R=[1/(2^(k-1)) , 1]

But... that's the same thing.
And the range seems to be incorrect.

I know that's the same thing (always the shortest formula!), but the range is undoubtedly correct. I proved its right side (<=1) but the left side is still a mystery to me!

it's fianlly done!
But how can i write formulas like you?