What is the general solution for cos(θ)tan^2(θ)=3cos(θ) ?

The general solution for cos(θ)tan^2(θ)=3cos(θ) is θ=(2pi)/3+pin,θ= pi/3+pin

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cos(θ)tan^2(θ)=3cos(θ)

cos (θ) tan^{2} (θ) = 3 cos (θ)

θ = \frac{2 π}{3} + πn, θ = \frac{π}{3} + πn

Solution steps

cos (θ) tan^{2} (θ) = 3 cos (θ)

Subtract

3 cos (θ)

from both sides

tan^{2} (θ) cos (θ) - 3 cos (θ) = 0

Factor

tan^{2} (θ) cos (θ) - 3 cos (θ) : cos (θ) (tan (θ) + 3) (tan (θ) - 3)

cos (θ) (tan (θ) + 3) (tan (θ) - 3) = 0

Solving each part separately

cos (θ) = 0 or tan (θ) + 3 = 0 or tan (θ) - 3 = 0

cos (θ) = 0 : θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

tan (θ) + 3 = 0 : θ = \frac{2 π}{3} + πn

tan (θ) - 3 = 0 : θ = \frac{π}{3} + πn

Combine all the solutions

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn, θ = \frac{2 π}{3} + πn, θ = \frac{π}{3} + πn

Since the equation is undefined for:

\frac{π}{2} + 2 πn, \frac{3 π}{2} + 2 πn

θ = \frac{2 π}{3} + πn, θ = \frac{π}{3} + πn

cos (θ) = 0.56

cos (θ) = 0.17

sin (2 x) - 3 cos (x) = 0

5 cos (x) + 1 = 1

cosh (z) = 1

What is the general solution for cos(θ)tan^2(θ)=3cos(θ) ?
The general solution for cos(θ)tan^2(θ)=3cos(θ) is θ=(2pi)/3+pin,θ= pi/3+pin