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)#