Question #15b2e

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Answer 1 · 2017-10-15T00:24:40

In degrees:

$x = 30^{\circ}, 150^{\circ}, 210^{\circ}, 330^{\circ}$ $x=30^@, 150^@, 210^@, 330^@$

In radians:

$x = \frac{π}{6}, \frac{5 π}{6}, \frac{7 π}{6}, \frac{11 π}{6}$ $x=pi/6, (5pi)/6, (7pi)/6, (11pi)/6$

${sec}^{2} x - 2 {tan}^{2} x = \frac{2}{3}$ $sec^2x-2tan^2x=2/3$

We know that ${sec}^{2} x = 1 + {tan}^{2} x$ $sec^2x=1+tan^2x$ :

$1 + {tan}^{2} x - 2 {tan}^{2} x = \frac{2}{3}$ $1+tan^2x-2tan^2x=2/3$

Simplifying:

$- {tan}^{2} x = \frac{2}{3} - 1$ $-tan^2x=2/3-1$

$- {tan}^{2} x = - \frac{1}{3}$ $-tan^2x=-1/3$

${tan}^{2} x = \frac{1}{3}$ $tan^2x=1/3$

$tan x = \pm \frac{1}{\sqrt{3}}$ $tanx=+-1/sqrt(3)$

In degrees:

$therefore x=30^@, 150^@, 210^@, 330^@$

In radians:

$therefore x=pi/6, (5pi)/6, (7pi)/6, (11pi)/6$