Question

if 5sin tita =12cos teta find the value of sec teta​

Answer 1

Step-by-step explanation:

Mark brainlist

$5 sinc \: teta = \: 12 \: cos \: teta............(given) \: eq \: (1)$

$from \: eq(1) \: we \: get \\ \frac{sin \: teta}{cos \: teta} = \frac{12}{5}$

$we \: know \: \\ tan \: teta \: = \frac{sin \: teta}{cos \: teta} = \frac{opposite}{adjacent} \\ \:$

$therefore \: \\ \: we \: got \\ opposite \: = 12 \\ adjacent \: = 5$

By applying Pythagoras theorem

${h}^{2} = {s1}^{2} + {s2}^{2} \\ \: \: \: = {12}^{2} + {5}^{2} \\ \: \: \: \: \: = 144 + 25 \\ \: \: \: \: \: \: \: \: = 169 \\ {h}^{2} = 169 \\ h = 13 \\ therefore \\ hypotenus \: = 13$

$for \: sec \: teta \: \: \\ we \: have \: formula \\ sec \: teta = \frac{hypotenus}{adjacent } \\ \: sec \: teta \: = \frac{13}{5}$