Frequency response equalizer

Question

I have $ H_{tot} (f) = e^{-i 2 \pi f T } $ if $ |f| < \frac{1}{2T} $ and ‘ it doesn’t matter ‘ if $ |f| > \frac{1}{2T} $ and $ H(f) = (1 + 2a cos (2 \pi f T )) e^{-i 2 \pi f T } $ and I have to find the frequency response of the equalizer. I know from theory that $ \frac{H_{tot} (f) }{H (f) } = H_{eq}(f) $ and I found that $ H_{eq } (f) = \frac{1}{1 + 2acos(2 \pi f T } $. This is correct but now my book also write that this is also equal to $ \frac{1}{A_H (f) } rect (fT) $ Thank you !