Question

If sec theta + tan theta = p, show that p^2+1/ 2p = sec theta.

Answer 1

Step-by-step explanation:

Given : secθ + tanθ = p ...(i)

We know that,

sec²θ - tan²θ = 1

(secθ + tanθ)(secθ - tanθ) = 1

p(secθ - tanθ) = 1

secθ - tanθ = 1/p ...(ii)

Adding (i) and (ii), we get

2secθ = p + 1/p

2secθ = (p² + 1)/p

secθ = (p² + 1)/2p

Hence, proved !!