Question

if sec theta + tan tetha=5 then cos theta is what​

Answer 1

Answer:

$cos \: theta = \frac{5}{13}$

Step-by-step explanation:

$\sec \: theta + tan \: theta = 5$

$tan \: theta = 5 - sec \: theta$

take square on both sides,

${tan}^{2} theta = 25 + {sec}^{2} theta - 10sec \: theta$

we know that

${tan}^{2} theta = {sec}^{2} theta - 1$

therefore,

${sec}^{2} theta - 1 = 25 + {sec}^{2} theta - 10sec \: theta$

$10sec \: theta = 26$

$sec \: theta = \frac{26}{10}$

$sec \: theta = \frac{13}{5}$

we know that,

1/cos theta = sec theta

$cos \: theta = \frac{5}{13}$