Question

tan square x + cot square x = 2

Answer 1

The equation here is \[\tan^2(x) + \cot^2(x) = 2\] which only happens when tangent and cotangent are either both 1, or both -1. Since cotanget = 1/tangent, we just have to find the places where tangent is 1 or -1. Those angles are:
\[theta = \pi/4, 3\pi/4, 5\pi/4, 7\pi/4,...\]
Depending on how this question is asked, you'll want to give the answers in different ways. Those angles listed above are all the solutions between 0 and 2pi. The general solution is: \[theta = \pi/4 + k \pi\] for integer values k.