Given s and g are positive integers and $cos\theta$ and $sin\theta$ are rational and not equal to 0 or 1. Show these 3 expressions cannot all be perfect squares:
$$s^2+2g^2-2sg(cos\theta-sin\theta)$$ $$s^2+g^2-2sg(cos\theta)$$ $$s^2+g^2+2sg(sin\theta)$$
Appreciate any tips.