Question

find sec x if sec x-tan x=3/4​

Answer 1

GIVEN :-

sec x-tan x=3/4

TO FIND :-

sec x

FORMULA USED :-

$sec ^{2} (x) - {tan}^{2} (x) = 1$

SOLUTION :-

$sec ^{2} (x) - {tan}^{2} (x) = 1$

$(sec (x) + tan(x))(sec (x) - tan(x)) = 1$

$sec (x) - tan(x) = \frac{3}{4} \: \: equation \: 1 \: \: \\ (sec (x) + tan(x))( \frac{3}{4} ) = 1 \\ sec (x) + tan(x) = \frac{4}{3} \: equation \: 2$

$adding \: equation \: 1 \: and \: 2 \\ we \: get \\ 2 \times sec(x) = \frac{3}{4} + \frac{4}{3} = \frac{25}{12} \\ sec(x) = \frac{25}{24}$

ANSWER :-

$sec(x) = \frac{25}{24}$

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