What is the general solution for tan(x)+tan(2x)=0 ?

The general solution for tan(x)+tan(2x)=0 is x=pin,x=(2pi)/3+pin,x= pi/3+pin

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tan(x)+tan(2x)=0

tan (x) + tan (2 x) = 0

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

Solution steps

tan (x) + tan (2 x) = 0

Rewrite using trig identities

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

Solve by substitution

tan (x) = 0, tan (x) = - 3, tan (x) = 3

tan (x) = 0 : x = πn

tan (x) = - 3 : x = \frac{2 π}{3} + πn

tan (x) = 3 : x = \frac{π}{3} + πn

Combine all the solutions

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

3 cos (2 θ) + 2 = - cos (θ)

cos (x) = \frac{7.2}{9.4}

sin (θ) = - 2 - cos (θ)

sin (2 θ) = 3 cos (2 θ)

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

What is the general solution for tan(x)+tan(2x)=0 ?
The general solution for tan(x)+tan(2x)=0 is x=pin,x=(2pi)/3+pin,x= pi/3+pin