How do you find ALL solutions for the equation tan^2 (x) = -tan (x)?

1 Answer
Nghi N. · Kevin B.
Apr 17, 2015

f(x) = tan^2 x + tan x = tan x*(1 + tan x) = 0.

Next solve the 2 basic trig equations: tan x = 0 and tan x = -1

  1. tan x = 0 --> x = 0 and x = pi
  2. tan x = -1 --> x = (3pi)/4 and x = (2pi - pi/4) = (7pi)/4.

Answers inside interval (0, 2pi): 0; (3pi)/4, pi; and 7pi/4.
Extended answers: x = K*pi; and x = 3pi/4 + k*pi.

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