Question #15b2e

1 Answer
Oct 15, 2017

In degrees:

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

In radians:

x=pi/6, (5pi)/6, (7pi)/6, (11pi)/6x=π6,5π6,7π6,11π6

Explanation:

sec^2x-2tan^2x=2/3sec2x2tan2x=23

We know that sec^2x=1+tan^2xsec2x=1+tan2x:

1+tan^2x-2tan^2x=2/31+tan2x2tan2x=23

Simplifying:

-tan^2x=2/3-1tan2x=231

-tan^2x=-1/3tan2x=13

tan^2x=1/3tan2x=13

tanx=+-1/sqrt(3)tanx=±13

In degrees:

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

In radians:

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