Tan(3theta-45)=½

Question

Tan(3theta-45)=½

Answer 1

It's not an identity; it's a conditional equation to be solved.

first, arctan 0.5 = 26.565^o or 126.565^o (there are other solutions, equal to these + ANY multiple of 360 deg.).

 

Therefore 26.565 + k•180 = 3θ - 45 and you can solve for θ.  There are infinitely many solutions because when you solve for theta you'll be dividing the optional extra 180s by 3.