exact simplified solution

Question

Find an exact simplified solution to the equation below so that 0 < θ < π/5.
1 = √3 *tan(5θ)

Answer 1

1 = √3tan(5θ)

 

tan(5θ) = 1/√3

 

5θ = π/6 + kπ, k = 0, ±1, ±2,...

 

θ = π/30 + kπ/5

 

If k = 0, then θ = π/30

 

For all other values of k, θ lies outside of the interval (0, π/5).

 

The only solution in the given interval is π/30.