Question

if sec theta + tan theta is equal to p then find the value of tan theta ​

Answer 1

Answer:

$tan \ \theta = \frac{p^2-1}{2p}$

Step-by-step explanation:

Given :

$sec \ \theta + tan \ \theta = p$ ....(1)

To find :

The value of $tan \ \theta$

we know that,

$sec^2 \ \theta - tan^2 \ \theta = 1$

⇒ $(sec \ \theta - tan \ \theta)(sec \ \theta + tan \ \theta) = 1$    As, ∵ a² - b² = (a + b)(a - b)

⇒ $(sec \ \theta - tan \ \theta)(p) = 1$

⇒ $sec \ \theta - tan \ \theta = \frac{1}{p}$  ....(2)

By  subtracting (2) from (1),

We get,

⇒ $(sec \ \theta + tan \ \theta) - (sec \ \theta - tan \ \theta) = p - \frac{1}{p}$

⇒ $sec \ \theta + tan \ \theta - sec \ \theta + tan \ \theta = \frac{p^2-1}{p}$

⇒ $2 \ tan \ \theta = \frac{p^2-1}{p}$

⇒ $tan \ \theta = \frac{p^2-1}{2p}$