Tanx = cotx

Question

Solve this equation for 0< or equal to x< or equal to 2pi.

Answer 1

tan(x) = cot(x)
tan(x) - cot(x) = 0
(sin(x) / cos(x)) - (cos(x) / sin(x)) = 0
(sin^2(x) / sin(x)cos(x)) - (cos^2(x) / sin(x)cos(x)) = 0
(sin^2(x) - cos^2(x)) / (sin(x)cos(x)) = 0
sin^2(x) - cos^2(x) = 0
cos^2(x) - sin^2(x) = 0
cos(2x) = 0

Note that if 0 <= x <= 2pi, then 0 <= 2x <= 4pi
If cos(2x) = 0 on [0, 4pi]. we have:

2x = pi/2 or 3pi/2 or 5pi/2 or 7pi/2
x = pi/4 or 3pi/4 or 5pi/4 or 7pi/4