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

The general solution for (tan(2θ))/2 =tan(θ) is θ=pin

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(tan(2θ))/2 =tan(θ)

\frac{tan ( 2 θ )}{2} = tan (θ)

θ = πn

Solution steps

\frac{tan ( 2 θ )}{2} = tan (θ)

Subtract

tan (θ)

from both sides

\frac{tan ( 2 θ )}{2} - tan (θ) = 0

Simplify

\frac{tan ( 2 θ )}{2} - tan (θ) : \frac{tan ( 2 θ ) - 2 tan ( θ )}{2}

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

tan (2 θ) - 2 tan (θ) = 0

Rewrite using trig identities

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

Solve by substitution

tan (θ) = 0

tan (θ) = 0 : θ = πn

Combine all the solutions

θ = πn

2 sin^{2} (3 x) - 3 cos (3 x) + 1 = 0, 0^{\circ} \leq x \leq 18 0^{\circ}

2 sin (\frac{x}{2}) = 1 - cos (x)

sin (x) = \frac{- sin ( 2 x )}{2}

12 sin (A) + 4 = 4 sin (A) + 4

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

What is the general solution for (tan(2θ))/2 =tan(θ) ?
The general solution for (tan(2θ))/2 =tan(θ) is θ=pin