Question #15b2e

1 Answer
Oct 15, 2017

In degrees:

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

In radians:

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

Explanation:

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

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

1+tan^2x-2tan^2x=2/3

Simplifying:

-tan^2x=2/3-1

-tan^2x=-1/3

tan^2x=1/3

tanx=+-1/sqrt(3)

In degrees:

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

In radians:

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