Question

if sec theta+tan theta=p then prove tan theta = p^2 -1÷2p​

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)

Subtracting (i) and (ii), we get

2tanθ = p - 1/p

2tanθ = (p² - 1)/p

tanθ = (p² - 1)/2p

Hence, proved !!