Question

if secA=13/12,find tanA and sinA

Answer 1

Answer:

$given : sec \: a = \frac{13}{12} \\ \\ proof : tan \: a = ? \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: sin \: a = ? \\ \\ solution : \\ \\ sec \: a = \frac{h}{b} = \frac{13}{12} \\ \\ { h}^{2} = {b}^{2} + {p}^{2} \\ \\ {13}^{2} = {12}^{2} + p^{2} \\ \\ 169 = 144 + {p}^{2} \\ \\ 169 - 144 = {p}^{2} \\ \\ 25 = {p}^{2} \\ \\ p = \sqrt{25} \\ \\ p = 5 \\ \\ now \\ \\ sin \: a = \frac{p}{h} = \frac{5}{13} \\ \\ and \\ \\ tan \: a = \frac{p}{b} = \frac{5}{12}$

Hence proved.