Question

if 5cot 0=12 find the value of coseco+seco?​

Answer 1

SOLUTION :

$\bull \: \: \: \: \: \: \: { \underline{ \underline{ \sf \: 5 \cot \theta = 12}}} \\ = > \sf \: \cot \theta = \frac{12}{5} \\ = > { \cot}^{2} \theta = \frac{144}{25} \\ = > { \cosec}^{2} \theta - 1 = \frac{144}{25} \\ = > \cosec \theta = \frac{13}{5} \underline{ \: \: \: \: \: \: \: \: }(1)$

$\underline{ \tt \:{from \: eqn \: 1}}$

$\cosec \theta = \frac{13}{5} \\ = > { \sin}^{2} \theta = \frac{25}{169} \\ = > 1 - { \cos}^{2} \theta = \frac{25}{169} \\ = > \cos \theta = \frac{12}{13} \underline{ \: \: \: \: \: \: \: \: \: \: \: }(2)$

$\underline{ \tt{adding \: eqn \: (1) \: and \: (2)}}$

$\cosec \theta \: + \sec \theta \\ = \frac{13}{5} + \frac{12}{13} \\ = \boxed{ \frac{229}{65} }$