Question

if tan theta +sec theta=p then prove that sec theta = (p^2+1)/2p

Answer 1

Given secθ + tanθ = p----(1)
As sec²θ-tan²θ= 1,
(secθ+tanθ)(secθ-tanθ)=1
⇒secθ-tanθ=1/p-----(2)
(1)+(2)⇒2secθ=(p²+1)/p
⇒secθ=(p²+1)/2p
Hence,proved.