Question

Given that
$sec( \alpha) - tan( \alpha ) = \frac{1}{4} \: find \: \sec( \alpha ) + \tan( \alpha )$
​

Answer 1

Answer:

4.

Step-by-step explanation:

(sec α - tan α)(sec α + tan α) = sec^2 α - tan^2α

But sec^2  α = 1 + tan^2 α so

sec^2 α - tan^2α  = 1 + tan^2 α - tan^2α

= 1

so 1 =  (sec α - tan α)(sec α + tan α) = 1/4 * x     where x  is sec α + tan α

1/4 * x = 1

x = 4.