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Hello, in the part to replace cos45 if I write sq root 2 / 2 (that is what the calculator gives me) instead of 1 / sq root of 2, at the end I guess it will give me a different answer. Right?

Hello cm2hn, thanks for your question. Well, the ultimate proof is always in trying your variation and see the effect, but I can say that $\dfrac{1}{\sqrt{2}} = \dfrac{\sqrt{2}}{2}$. If you multiply $\dfrac{1}{\sqrt{2}}$ by "1", you won't change it's value, but if you make "1" look funny as, say, $\dfrac{\sqrt{2}}{\sqrt{2}}$, you'll find that it turns $\dfrac{1}{\sqrt{2}} $ into $\dfrac{\sqrt{2}}{2}$. We know that they're equivalent since you can turn one into the other by multiplying by 1.
All the best,
Mr. Dychko