Question

How do you find the general solutions for `Tan^2β = tanβ`?

Answer 1

The equation may be written as `tan^2beta - tanbeta = 0`
or `tan beta * (tan beta - 1) = 0`
Hence `tanbeta = 0 or (tanbeta - 1) = 0`
If `tanbeta = 0` then `beta = npi`, where `n = 0,1,2` . . .etc
Or if `tanbeta - 1 = 0` then `tan beta = 1` or `beta = pi / 4 + n * pi`