Question

puteti va rog sa rezolvati:
sin 1/14 x = cos^4 1/28 x - sin^4 1/28 x
raspunsul daca este posibil de trecut in grade

Answer 1

Răspuns:

Explicație pas cu pas:

$cos^4\frac{x}{28}-sin^4\frac{x}{28}=\\ \\ =(cos^2 \frac{x}{28} + sin^2\frac{x}{28})(cos^2\frac{x}{28}-sin^2\frac{x}{28})=\\ \\=1\cdot(cos^2\frac{x}{28}-sin^2\frac{x}{28})=\\ \\ =cos(2\cdot \frac{x}{28})=\\ \\ =cos \frac{x}{14} \\ \\ \\sin\frac{x}{14}=cos\frac{x}{14}\\ \\ \Rightarrow tg \frac{x}{14}=1 \Rightarrow \frac{x}{14}=arctg1+\pi n,~n\in Z \Rightarrow \frac{x}{14}=\frac{\pi}{4}+\pi n;~(arctg1=\frac{\pi}{4}) \\ \\ \Rightarrow x=\frac{7\pi}{2}+14\pi n$