Question

if cosec theta + cot theta =5 then find the value of sec theta

Answer 1

Answer:

hope this will help you.

Answer 2

If cosec theta + cot theta = 5 then the value of $sec\ \theta = \frac{13}{12}$

Solution:

Given that,

$cosec\ \theta + cot\ \theta = 5 ---- eqn\ 1$

We know that, by identity,

$cosec^2\ \theta-cot^2\ \theta = 1$

$On\ expanding\ using\ a^2-b^2=(a+b)(a-b)$

$(cosec\ \theta + cot\ \theta)(cosec\ \theta - cot\ \theta) = 1$

$Substitute\ cosec\ \theta + cot\ \theta = 5$

$5(cosec\ \theta -cot\ \theta) = 1\\\\cosec\ \theta -cot\ \theta = \frac{1}{5}\\\\cosec\ \theta -cot\ \theta = 0.2 ------ eqn\ 2$

Add eqn 1 and eqn 2

$cosec\ \theta + cot\ \theta + cosec\ \thtea - cot\ \theta = 5 + 0.2\\\\2cosec\ \theta = 5.2\\\\cosec\ \theta = 2.6 = \frac{13}{5}$

We know that,

$sin\ \theta = \frac{1}{cosec\ \theta}$

Therefore,

$sin\ \theta = \frac{5}{13}$

By identity,

$cos^2\ \theta = 1 - sin^2\ \theta\\\\cos^2\ \theta = 1 - (\frac{5}{13})^2\\\\cos^2\ \theta = 1 - \frac{25}{169}\\\\cos^2\ \theta = \frac{144}{169}\\\\Take\ square\ root\ on\ both\ sides\\\\cos\ \theta = \frac{12}{13}\\\\We\ know\ that\\\\sec\ \theta= \frac{1}{cos\ \theta}\\\\sec\ \theta = \frac{13}{12}$

Thus the value of sec theta is found

Learn more about this topic

If cosec theta +cot theta =p, then find cos theta in terms of p

https://brainly.in/question/6804334

If cosec theta + cot theta = k prove that cos theta = k2-1 / k2 + 1

https://brainly.in/question/1420648