if tan10x=cot5x, then what is the value of x?

Answer 1

tan10x = 2tan5x/(1-tan^2(5x))
so,

2tan(5x)/(1-tan^2(5x)) = 1/tan(5x)
2tan^2(5x) = 1-tan^2(5x)
3tan^2(5x) = 1
tan 5x = ±1/√3

Now use that to get your reference angles and produce as many solutions as your domain requires.

Answer 2

Tan10x=cot5x