What is the general solution for 4tan(2x)-4cot(x)=0 ?

The general solution for 4tan(2x)-4cot(x)=0 is x=0.52359…+pin,x=-0.52359…+pin

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4tan(2x)-4cot(x)=0

4 tan (2 x) - 4 cot (x) = 0

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

Solution steps

4 tan (2 x) - 4 cot (x) = 0

Rewrite using trig identities

- \frac{- 4 + 12 tan ^{2} ( x )}{( - 1 + tan ( x ) ) ( 1 + tan ( x ) ) tan ( 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

sin (x) = \frac{24}{25}

arcsin (3 x - π) = \frac{1}{2}

2 cos^{2} (θ) + sin (θ) - 1 = 0

2 sin (2 x) sin (x) - 3 cos (x) = 0

sin (θ) = \frac{13}{7}

What is the general solution for 4tan(2x)-4cot(x)=0 ?
The general solution for 4tan(2x)-4cot(x)=0 is x=0.52359…+pin,x=-0.52359…+pin