Question

Find all solutions of the following equation in the interval (0,2π).
tanx-cotx=0

Answer 1

tan(x)=cot(x)
tan(x)=[1/tan(x)]
[tan(x)]^2=1

Since anything times 1 is itself, tan(x) must be 1 otherwise tan(x)^2 wouldn't be 1. However, the squared allows for tan(x) to also be -1.
The values of tan(x) that are 1 or -1 within the interval given are x=π/4, 3π/4, 5π/4, 7π/4. These are just the values when the absolute value of sin and cos are the same.