Given that sec( \alpha) - tan( \alpha ) = (1)/(4) \: find \: \sec( \alpha ) + \tan( \alpha ) ​

Question

Given that


`sec( \alpha) - tan( \alpha ) = (1)/(4) \: find \: \sec( \alpha ) + \tan( \alpha )`
​

Answer 1

4.

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.