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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.

Ameet Sharma
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  • Trigonometric functions - much in the way to solve the equation. Also not clear - are they independent or not? So it's best to write more formally using algebraic functions. – individ Dec 05 '15 at 06:12
  • 2 and 3 the equation is dependent from each other. This means this formulation to solve the problem is not correct. In this case, the number of decisions can be assured. – individ Dec 05 '15 at 06:23

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