Question

Solve tan5theta.tan3theta=1

Answer 1

tan 3θ=1/tan5θ

(0<θ<2π)

tan 3θ=cot5θ

tan 3θ=tan(π/2 -5θ)

3θ=π/2 -5θ, 3π/2 -5θ, 5π/2 -5θ,7π/2 -5θ, .....31π/2 -5θ,

8θ=π/2 , 3π/2 , 5π/2 ,7π/2 , .....31π/2

θ=π/16 , 3π/16 , 5π/16 ,7π/16 , .....31π/16