Question #15b2e

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Answer 1 · 2017-10-15T00:24:40

In degrees:

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

In radians:

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

#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#