Question

in a right angled triangle A is an acute angle and tan A = 5/12 . find cosA+sinA÷ cosA-sinA​

Answer 1

Step-by-step explanation:

tan A =opp/adj = 5/12

using pythagoras theorem

${hyp}^{2} = {opp}^{2} + {adj}^{2} \\ {hyp}^{2} = {5}^{2} + {12}^{2} \\ {hyp}^{2} = 25 + 144 \\ {hyp}^{2} = 169 \\ hyp = \sqrt{169} = 13$

sin A = 5/13

cos A = 12/13

$= \frac{ \frac{12}{13} + \frac{5}{13} }{ \frac{12}{13} - \frac{5}{13} } \\ = \frac{ \frac{12 + 5}{13} }{ \frac{12 - 5}{13} } \\ = \frac{12 + 5}{13} \times \frac{13}{12 - 5} \\ = \frac{12 + 5}{12 - 5} \\ = \frac{17}{7}$

hope you get your answer