The number of principal solutions of tan 2 θ = 1 is

If the equation involves a variable 0 ≤ x < 2π, then the solutions are called principal solutions.

tan^-1 (1) = 

Calculations:

Given tan 2θ = 1

⇒ 2θ = tan -1 (1)

⇒ 2θ =  

⇒ θ =  

for principal solution 0 ≤ θ < 2π

Hence,θ =   

The number of principal solutions of tan 2 θ = 1 is four