Which one of the following is a value of θ, if θ satisfies the equation tan 2θ tan 4θ − 1 = 0; 0

Question

Which one of the following is a value of θ, if θ satisfies the equation tan 2θ tan 4θ − 1 = 0; 0 < θ < π/2?

Accepted Answer

π/12. tan2θ·tan4θ = 1 ⟹ tan4θ = cot2θ = tan(π/2−2θ). So 4θ = π/2−2θ + nπ, giving 6θ = π/2, θ = π/12.

Which one of the following is a value of θ, if θ satisfies the equation tan 2θ tan 4θ − 1 = 0; 0 < θ < π/2?