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#