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

The general solution for 3tan(θ)=tan(2θ) is θ=pin,θ=(5pi)/6+pin,θ= pi/6+pin

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3tan(θ)=tan(2θ)

3 tan (θ) = tan (2 θ)

θ = πn, θ = \frac{5 π}{6} + πn, θ = \frac{π}{6} + πn

Solution steps

3 tan (θ) = tan (2 θ)

Subtract

tan (2 θ)

from both sides

3 tan (θ) - tan (2 θ) = 0

Rewrite using trig identities

\frac{tan ( θ ) - 3 tan ^{3} ( θ )}{1 - tan ^{2} ( θ )} = 0

Solve by substitution

tan (θ) = 0, tan (θ) = - \frac{3}{3}, tan (θ) = \frac{3}{3}

tan (θ) = 0 : θ = πn

tan (θ) = - \frac{3}{3} : θ = \frac{5 π}{6} + πn

tan (θ) = \frac{3}{3} : θ = \frac{π}{6} + πn

Combine all the solutions

θ = πn, θ = \frac{5 π}{6} + πn, θ = \frac{π}{6} + πn

cos^{(2)} (x) - 3 sin^{(2)} (x) = 0

a, cos (a) cos (b) = 0.426

5 cos (x) - 4 = 0

2 + 2 cos (x) = 2 - 2 sin (x)

sin (x) = 14

What is the general solution for 3tan(θ)=tan(2θ) ?
The general solution for 3tan(θ)=tan(2θ) is θ=pin,θ=(5pi)/6+pin,θ= pi/6+pin