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

The general solution for tan(2x)-cot(x)=0 is x= pi/6+(2pin)/3 ,x= pi/2+(2pin)/3

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

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

x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}

Solution steps

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

Express with sin, cos

\frac{- cos ( 2 x ) cos ( x ) + sin ( 2 x ) sin ( x )}{cos ( 2 x ) sin ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Rewrite using trig identities

- cos (2 x + x) = 0

Divide both sides by

- 1

cos (2 x + x) = 0

General solutions for

cos (2 x + x) = 0

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

Solve

2 x + x = \frac{π}{2} + 2 πn : x = \frac{π}{6} + \frac{2 πn}{3}

Solve

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

x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}

sin (x) = \frac{3}{4}

2 sin (\frac{x}{4}) + 3 = 0

sin (2 θ) = cos (θ)

sin (θ) = \frac{2}{3}

sin (2 θ) = 0

What is the general solution for tan(2x)-cot(x)=0 ?
The general solution for tan(2x)-cot(x)=0 is x= pi/6+(2pin)/3 ,x= pi/2+(2pin)/3