if sec A+ tan A= x, then tan x is equal to?

Given, sec A + tan A = x                  ... (1)

 

Now, we know the identity 1 + tan²A = sec²A

sec²A - tan²A = 1

(secA - tanA) (sec A + tanA) = 1          [Using the identity: a² - b² = (a - b)(a + b)]

secA - tanA = 1/x           ... (2)      [Using the given equation (1)]

 

Now, subtract (2) from (1), we get,

2 tan A = x - 1/x = (x² - 1) /x

Thus, tan A = (x² - 1) /2x