Question

Вычислите: sin(2arccos5/13)

Answer 1

$sin(2arccos \frac{5}{13})=2sin(arccos \frac{5}{13})*cos(arccos \frac{5}{13})=\\\\=2* \frac{ \sqrt{13^2-5^2} }{13}* \frac{5}{13}=10* \frac{ \sqrt{169-25} }{169}= \frac{10 \sqrt{144} }{169}= \frac{10*12}{169}= \frac{120}{169}$