Question

if sec theta = p+1/4p then find the value of sec theta +tan theta

Answer 1

1 + $tan^{2}$x = $sec ^{2}$x

tan x = √$sec ^{2}$x - 1 
   
         = √(p+ 1/4p)² - 1
         
         = p + 1/4p - 1
   
          
Thus,
   
   sec x + tan x =  p + 1/4p + p + 1/4p - 1

                         = 2p + 1/2p - 1

Answer 2

Answer:

$\sec\theta+\tan\theta=2p$

Step-by-step explanation:

Given : $\sec\theta=p+\frac{1}{4p}$

To find : The value of $\sec\theta+\tan\theta$ ?

Solution :

Write the expression as,

$\sec\theta+\tan\theta=\sec\theta+\sqrt{\sec^2\theta-1}$

Substitute, $\sec\theta=p+\frac{1}{4p}$

$\sec\theta+\tan\theta=(p+\frac{1}{4p})+\sqrt{(p+\frac{1}{4p})^2-1}$

$\sec\theta+\tan\theta=(p+\frac{1}{4p})+\sqrt{(p+\frac{1}{4p})^2-4\times p\times \frac{1}{p}}$

We know, $(a+b)^2-4ab=(a-b)^2$

$\sec\theta+\tan\theta=(p+\frac{1}{4p})+\sqrt{(p-\frac{1}{4p})^2}$

$\sec\theta+\tan\theta=(p+\frac{1}{4p})+(p-\frac{1}{4p})$

$\sec\theta+\tan\theta=2p$