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Answer 1 · 2016-10-31T21:22:40

#sec^2x + 2tanx - 3= 0#

Recall the pythagorean identity #sec^2theta = 1 + tan^2theta#.

#1 + tan^2x +2tanx - 3 = 0#

#tan^2x + 2tanx - 2 = 0#

Let #t = tanx#

#t^2 + 2t - 2 = 0#

#t = (-2 +- sqrt(2^2 - 4 xx 1 xx -2))/(2 xx 1)#

#t = (-2 +-sqrt(12))/2#

#t = (-2 +- 2sqrt(3))/2#

#t = -1 +- sqrt(3)#

#tanx = -1 +- sqrt(3)#

#x = pin - arctan(sqrt(3)-1) and pin - arctan(1 + sqrt(3))#

Hopefully this helps!