What is the general solution for 3cot(2x)-1=0 ?

The general solution for 3cot(2x)-1=0 is x=(1.24904…)/2+(pin)/2

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3cot(2x)-1=0

3 cot (2 x) - 1 = 0

x = \frac{1.24904 \dots}{2} + \frac{πn}{2}

Degrees

x = 35.78252 \dots^{\circ} + 9 0^{\circ} n

Solution steps

3 cot (2 x) - 1 = 0

Move

1

to the right side

3 cot (2 x) - 1 = 0

Add

1

to both sides

3 cot (2 x) - 1 + 1 = 0 + 1

Simplify

3 cot (2 x) = 1

3 cot (2 x) = 1

Divide both sides by

3

3 cot (2 x) = 1

Divide both sides by

3

\frac{3 cot ( 2 x )}{3} = \frac{1}{3}

Simplify

cot (2 x) = \frac{1}{3}

cot (2 x) = \frac{1}{3}

Apply trig inverse properties

cot (2 x) = \frac{1}{3}

General solutions for

cot (2 x) = \frac{1}{3}

cot (x) = a \Rightarrow x = arccot (a) + πn

2 x = arccot (\frac{1}{3}) + πn

2 x = arccot (\frac{1}{3}) + πn

Solve

2 x = arccot (\frac{1}{3}) + πn : x = \frac{arccot ( \frac{1}{3} )}{2} + \frac{πn}{2}

2 x = arccot (\frac{1}{3}) + πn

Divide both sides by

2

2 x = arccot (\frac{1}{3}) + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arccot ( \frac{1}{3} )}{2} + \frac{πn}{2}

Simplify

x = \frac{arccot ( \frac{1}{3} )}{2} + \frac{πn}{2}

x = \frac{arccot ( \frac{1}{3} )}{2} + \frac{πn}{2}

x = \frac{arccot ( \frac{1}{3} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{1.24904 \dots}{2} + \frac{πn}{2}

sec (x) = tan (x) - 1

tan (θ) = \frac{5}{4}

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

tan^{2} (θ) - 3 tan (θ) = 0

x, tan (x) = 0

What is the general solution for 3cot(2x)-1=0 ?
The general solution for 3cot(2x)-1=0 is x=(1.24904…)/2+(pin)/2