What is the general solution for tan(3x)(tan(x)-1)=0 ?

The general solution for tan(3x)(tan(x)-1)=0 is x=(pin)/3 ,x= pi/4+pin

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tan(3x)(tan(x)-1)=0

tan (3 x) (tan (x) - 1) = 0

x = \frac{πn}{3}, x = \frac{π}{4} + πn

Solution steps

tan (3 x) (tan (x) - 1) = 0

Solving each part separately

tan (3 x) = 0 or tan (x) - 1 = 0

tan (3 x) = 0 : x = \frac{πn}{3}

tan (x) - 1 = 0 : x = \frac{π}{4} + πn

Combine all the solutions

x = \frac{πn}{3}, x = \frac{π}{4} + πn

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

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

2 sin (2 x) = 1, 0 \leq x \leq 2 π

sin (θ) = \frac{1}{4}

2 sin (θ) + 3 = 2

What is the general solution for tan(3x)(tan(x)-1)=0 ?
The general solution for tan(3x)(tan(x)-1)=0 is x=(pin)/3 ,x= pi/4+pin