How do you solve #cot^2x - tan^2x = 0 #?

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May 2, 2015

Solution

# cot^2x-tan^2x = 0#
# y = tan x; 1/y =cot x#
# 1/y^2-y^2 =0#
#y^4-1 = 0#
#(y^2+1)(y^2-1)=0#
#y^2 = +- 1#
If #y^2 = 1# then #tan x = +-1#
#y^2 = -1# does not have real solution. But in terms of imaginary parts we have #tan x = +-i#

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How do you solve #cot^2x - tan^2x = 0 #?

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