How do you find all the solutions for #(2 (tan^2)x - 1)((tan^2)x +1) = 0#?

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Answer 1 · 2016-06-29T15:09:31

#x=35.26438968^@+-n*180" "#where #n=0, 1, 2, 3, 4....#

#x=144.7356103172^@+-n*180" "#where #n=0, 1, 2, 3, 4....#

the given trigonometric equation is

#(2*tan^2 x-1)(tan^2 x+1)=0#

using the first factor
#2*tan^2 x-1=0#

#tan^2 x=1/2#

#tan x=+-sqrt(1/2)=+-sqrt2/2#

#x=35.26438968^@+-n*180" "#where #n=0, 1, 2, 3, 4....#

#x=144.7356103172^@+-n*180" "#where #n=0, 1, 2, 3, 4....#

using the second factor

#tan^2 x+1=0#

#tan^2 x=-1#

#x= tan^-1 i#

No value for x

God bless....I hope the explanation is useful.