Level:
Project ID:
1003108809
Accepted:
1
Clonable:
0
Easy:
0
We are given the equation
\[ \sum\limits_{n=1}^{\infty} (\sin x)^{2n-2}=2\cdot\,\mathrm{tg}\,x \]
with the unknown \( x \) being a real number. What is the set of all its solutions?
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{\frac14\pi+k\cdot\pi\right\} \)
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{\frac34\pi+k\cdot\pi\right\} \)
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{\frac34\pi+k\cdot\frac{\pi}2\right\} \)
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{\frac18\pi+k\cdot\frac{\pi}2\right\} \)
\( \bigcup\limits_{k\in\mathbb{Z}}\left\{\frac14\pi+k\cdot\frac{\pi}2\right\} \)