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

Asked by  | 4th May, 2013, 08:53: PM

Expert Answer:

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

Answered by  | 5th May, 2013, 03:07: PM

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