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

The general solution for cot(x)tan(2x)=3 is x=0.52359…+pin,x=-0.52359…+pin

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cot(x)tan(2x)=3

cot (x) tan (2 x) = 3

x = 0.52359 \dots + πn, x = - 0.52359 \dots + πn

Solution steps

cot (x) tan (2 x) = 3

Subtract

3

from both sides

cot (x) tan (2 x) - 3 = 0

Rewrite using trig identities

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

Solve by substitution

tan (x) = \frac{1}{3}, tan (x) = - \frac{1}{3}

tan (x) = \frac{1}{3} : x = arctan (\frac{1}{3}) + πn

tan (x) = - \frac{1}{3} : x = arctan (- \frac{1}{3}) + πn

Combine all the solutions

x = arctan (\frac{1}{3}) + πn, x = arctan (- \frac{1}{3}) + πn

Show solutions in decimal form

x = 0.52359 \dots + πn, x = - 0.52359 \dots + πn

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

sin (3 x) = sin (5 x)

2 sin^{2} (3 θ) + sin (3 θ) - 1 = 0

4 cos (θ) + 3 = 2 cos (θ)

sin (2 x) = \frac{1}{2}, 0 \leq x < 2 π

What is the general solution for cot(x)tan(2x)=3 ?
The general solution for cot(x)tan(2x)=3 is x=0.52359…+pin,x=-0.52359…+pin