Question

if sec theta =13 then prove that sin theta =12/13

Answer 1

$\sec \theta = \frac{5}{13} \\ \sec \theta = \frac{1}{ \cos \theta } = \frac{13}{5} \\ \cos\theta = \frac{5}{13} \\ \sin \theta = \sqrt{1 - { \cos }^{2} } \theta \\ \sin \theta = \sqrt{1 - \frac{25}{169} } \\ \sin \theta = \sqrt{ \frac{169 - 25}{169} } \\ \\ \sin \theta = \sqrt{\frac{144}{169}} \\ \sin\theta = \frac{12}{13}$