Tan(theta)sec(theta)+2Tan(theta)=0

Question

solve the following 0<(or equal to) theta<2pi

Answer 1

tan(θ)sec(θ) + 2tan(θ) = 0 Begin by factoring out tan(θ):

tan(θ)[sec(θ) + 2] = 0 Now, using the Zero Product Rule, set each factor equal to zero:

1) tan(θ) = 0 which occurs at θ = 0 and θ = π

2) sec(θ) + 2 = 0

sec(θ) = -2

1/cos(θ) = -2

cos(θ) = -1/2 which occurs at θ = 2π/3 and 4π/3

So the solution then is θ = 0, 2π/3, π, 4π/3

Answer 2