Wait: $ \cos(2x) = \cos \pi = -1 $, $ \cos^2(2x) = 1 $, $ \sin^2 x = 1 $, so $ f(x) = 1 + 1 = 2 $? But that can’t be — maximum of each is 1, but sum could be 2? But let’s compute $ f(x) = \sin^2 x + \cos^2(2x) \leq 1 + 1 = 2 $, but is $ f(x) = 2 $ possible? Only if $ \sin^2 x = 1 $ and $ \cos^2(2x) = 1 $. - Abu Waleed Tea