If secθ - tanθ = p, then secθ is equal to:

If secθ - tanθ = p, then secθ is equal to: Correct Answer p/2 + 1/(2p)

Given that:

secθ - tanθ = p

Quantity used:

1 + tan²θ = sec²θ

calculation:

⇒ secθ - tanθ = p      ------(1)

multiply and divide equation (1) by (secθ + tanθ)

⇒ (secθ - tanθ)(secθ + tanθ)/(secθ + tanθ) = p

⇒ (sec²θ + secθtanθ - secθtanθ - tan²θ)/(secθ + tanθ) = p

⇒ (sec²θ - tan²θ)/(secθ + tanθ) = p

∵ sec2θ - tan2θ = 1

∴ 1/(secθ + tanθ) = p

⇒ secθ + tanθ = 1/p      ------(2)

Add equation(1) and (2)

⇒ secθ - tanθ + secθ - tanθ = p + 1/p

⇒ 2secθ = p + 1/p

∴ secθ = p/2 + 1/(2p)