What is the general solution for 1/2 tan(2θ)=tan(θ) ?

The general solution for 1/2 tan(2θ)=tan(θ) is θ=pin

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1/2 tan(2θ)=tan(θ)

\frac{1}{2} tan (2 θ) = tan (θ)

θ = πn

Solution steps

\frac{1}{2} tan (2 θ) = tan (θ)

Subtract

tan (θ)

from both sides

\frac{1}{2} tan (2 θ) - tan (θ) = 0

Simplify

\frac{1}{2} tan (2 θ) - 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

csc (x) - 3 = - 2 sin (x)

\frac{sin ( y )}{80} = \frac{sin ( 4 0 ^{\circ} )}{60}

cos (w) = 0.75 sin (9 0^{\circ} - w)

csc (4 x) = 2

3 tan^{2} (x) = 2 sec^{2} (x) + 1, 0^{\circ} \leq x \leq 18 0^{\circ}

What is the general solution for 1/2 tan(2θ)=tan(θ) ?
The general solution for 1/2 tan(2θ)=tan(θ) is θ=pin