If-sec-x-tan-x-sec-x-tan-x-5-then-what-is-the-value-of-3cos-2x-1-3cos-2x-1-

Question Number 128336 by liberty last updated on 06/Jan/21

If \frac{\sec x + \tan x}{\sec x - \tan x} = 5 then what is the

value of \frac{3 \cos 2 x + 1}{3 \cos 2 x - 1} ?

Answered by bramlexs22 last updated on 06/Jan/21

\Rightarrow \frac{\sec x + \tan x}{\sec x - \tan x} = 5

\Rightarrow \frac{\cos x (\sec x + \tan x)}{\cos x (\sec x - \tan x)} = 5

\Rightarrow \frac{1 + \sin x}{1 - \sin x} = 5; 1 + \sin x = 5 - 5 \sin x

\Rightarrow 6 \sin x = 4; \sin x = \frac{2}{3}

t h e n \frac{3 \cos 2 x + 1}{3 \cos 2 x - 1} = \frac{3 (1 - 2 \sin^{2} x) + 1}{3 (1 - 2 \sin^{2} x) - 1}

\Rightarrow \frac{4 - 2 (\frac{4}{9})}{2 - 2 (\frac{4}{9})} = \frac{2 - \frac{4}{9}}{1 - \frac{4}{9}} = \frac{14}{5} .