Calculus Question

Question

tan² x - tan x = 0

One set of answers is

a. π/4

b. π/4 , 3π/4

c. π/4, 5π/4

d. π/4 , 7π/4

My answer is a

Another set of answers is

a. π/2

b. 0

c. 0, π

d. π/2 , 3π/2

My answer is b

Answer 1

This is a factoring problem but also with an understanding of trig:

tan²x - tan x = 0

tan x (tan x – 1) = 0                                     Factor the equation

Solutions:

tan x = 0                                       or   tan x - 1 = 0

                                                             tan x = 1

x = 0 or 180                                        x = 45° or 225°

or  x = 0 or π                                 or    x = π/4 or x = 5π/4

Your answer needs to include all of the solutions for x. (Based on the options, the solutions are from 0 to 2π.)

Answer 2

tan²x - tan(x) = 0

tan(x) [tan(x) - 1] = 0

There are two possibilities:

tan(x) = 0 ⇒ x = 0 or π from the second set of choices (actually, x = nπ, where n is any integer)

or

tan(x) = 1 ⇒ from the first set of choices, both π/4 and 5π/4 are solutions