How do you solve #3tan^2x = 1#?

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Answer 1 · 2015-11-14T06:48:16

#x# = #30^o# , #150^o# , #210^0# , #330^0#

The given quadratic equation = #3tan^2# = #1#

#tan^2x# = #1/3#

Finding square root on both sides

#tanx# = #+-# #1/sqrt3#

Taking +ve value

#tanx# = #1/sqrt3#

#tanx# = #tan30^0#

#x# = #30^0#

since x is positive, x is positive in first or third quadrant

So, #x# = #30^0# or #180^0# + #30^0#
= #30^0# or #210^0#

Again taking -ve value

#tanx# = #-1/sqrt3#

Since tan will have negative value in second and fourth quadrant

#x# = #180-30# or #360-30#

#x# =#150^o# or #330^o#

Hence #x# = #30^o# , #150^o# , #210^0# , #330^0#