If $sec theta + tan theta = P$ , then what is $cos theta$ equal to?

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Answer 1 · 2016-11-27T11:28:22

Given $sectheta+tantheta=P....(1)$

we know

$sec^2theta-tan^2theta=1........(2)$

Dividing (2) by (1) we get

$sectheta-tantheta=1/P....(3)$

Now adding (1) and (3) we have

$2sectheta=P+1/P=(P^2+1)/P$

$=>sectheta=(P^2+1)/(2P)$

$=>costheta=(2P)/(P^2+1)$

If sec theta + tan theta = Psec theta + tan theta = P, then what is cos thetacos theta equal to?