Trig Question! Thank you in advance!

Question

Solve for x where pi ≤ x ≤ 2pi.

sin^2 x - cos^2 x / cos^2 x = 0

Answer 1

I am interpreting this problem with parenthesis around the numerator.

(sin²x-cos²x)/cos²x=0 Put both terms over the common denominator

sin²x/cos²x-cos²x/cos²x=0 Simplify

tan²x-1=0 Add 1 to both sides

tan²x-1+1=0+1 Simplify

tan²x=1 Take the square root of both sides

√tan²x=√1 Simplify

tan x = ±1 Solve

tan x = 1 at π/4 and 5π/4

tan x = -1 at 3π/4 and 7π/4

These are the 4 solutions for the given domain.