Question

Buna seara! Ma puteti ajuta cu aceasta problema?

Answer 1

Explicație pas cu pas:

$\sin^{2} (x) + \cos^{2} (x) = 1$

$\sin (2x) = 2\sin (x) \cos(x)$

$\cos(2x) = 2 \cos^{2} (x) - 1$

$\sin(x) = - \frac{12}{13} \\ \cos^{2} (x) = 1 - \sin^{2} (x) = 1 - (- \frac{12}{13})^{2} \\ = 1 - \frac{144}{169} = \frac{25}{169} \\ \frac{3\pi}{2} < x < 2\pi \\ = > \cos(x) = \frac{5}{13}$

$\cot(2x) = \frac{ \cos(2x) }{ \sin(2x) } = \frac{ 2\cos^{2} (x) - 1 }{2 \sin(x) \cos(x) } \\ = \frac{ \frac{2 + 25}{169} - 1 }{2 \times ( - \frac{12}{13}) \times \frac{5}{13} } \\ = \frac{50 - 169}{ - 2 \times 12 \times 5} = \frac{ - 119 }{ - 120}$

$= > \cot(2x) = \frac{119 }{120}$