What is the general solution for 9tan(2x)-9cot(x)=0 ?

The general solution for 9tan(2x)-9cot(x)=0 is x=0.52359…+pin,x=-0.52359…+pin

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9tan(2x)-9cot(x)=0

9 tan (2 x) - 9 cot (x) = 0

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

Solution steps

9 tan (2 x) - 9 cot (x) = 0

Rewrite using trig identities

- \frac{- 9 + 27 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 (2 x) = 2 sin^{2} (x)

sin (x) sec (x) = sin (x)

cos (x) + 2 = 0

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

sin (x) = \frac{3}{3}

What is the general solution for 9tan(2x)-9cot(x)=0 ?
The general solution for 9tan(2x)-9cot(x)=0 is x=0.52359…+pin,x=-0.52359…+pin