Question

if 5sec theta - 12 cosec theta =0 , find the value of cos theta , cot theta and sec theta​

Answer 1

$5 \sec \theta - 12 \: cosec \: \theta = 0 \\ 5 \sec \theta = 12 \: cosec \: \theta \\ \frac{5}{12} = \frac{cosec \: \theta}{ \sec \theta} - (i) \\ \frac{5}{12} = \frac{ \frac{1}{ \sin \theta} }{ \frac{1}{ \cos \theta} } \\ \frac{5}{12} = \frac{ \cos \theta }{ \sin \theta } \\ \boxed{\cot \theta = \frac{5}{12} } \\ {cosec}^{2} \theta = { \cot}^{2} \theta + 1 \\ cosec \: \theta = \sqrt{{ \cot}^{2} \theta + 1} \\ = \sqrt{ {( \frac{5}{12}) }^{2} + 1 } \\ = \sqrt{ \frac{25}{144} + 1} \\ = \sqrt{ \frac{169}{144} } \\ \boxed{cosec \: \theta = ±\frac{13}{12} } \\ \blue{\mathfrak{\underline{\large{from \: {eq}^{n} \: (i)}}}:} \\ \sec \theta = \frac{12}{5} cosec \: \theta \\ = \frac{12}{5} \times ± \frac{13}{12} \\ \boxed{ \sec \theta = ± \frac{13}{5} } \\ \boxed{ \cos \theta = ± \frac{5}{13} } \\ \\ \red{\mathfrak{\underline{\large{Hope \: It \: Helps \: You }}}} \\ \green{\mathfrak{\underline{\large{Mark \: Me \: Brainliest}}}}$