What is the general solution for 2cot^2(2x)=6 ?

The general solution for 2cot^2(2x)=6 is x= pi/(12)+(pin)/2 ,x=(5pi}{12}+\frac{pin)/2

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Popular >

2cot^2(2x)=6

Solution

2 cot^{2} (2 x) = 6

Solution

x = \frac{π}{12} + \frac{πn}{2}, x = \frac{5 π}{12} + \frac{πn}{2}

Degrees

x = 1 5^{\circ} + 9 0^{\circ} n, x = 7 5^{\circ} + 9 0^{\circ} n

Solution steps

2 cot^{2} (2 x) = 6

Solve by substitution

2 cot^{2} (2 x) = 6

Let:

cot (2 x) = u

2 u^{2} = 6

2 u^{2} = 6 : u = 3, u = - 3

2 u^{2} = 6

Divide both sides by

2

2 u^{2} = 6

Divide both sides by

2

\frac{2 u ^{2}}{2} = \frac{6}{2}

Simplify

u^{2} = 3

u^{2} = 3

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

u = 3, u = - 3

Substitute back

u = cot (2 x)

cot (2 x) = 3, cot (2 x) = - 3

cot (2 x) = 3, cot (2 x) = - 3

cot (2 x) = 3 : x = \frac{π}{12} + \frac{πn}{2}

cot (2 x) = 3

General solutions for

cot (2 x) = 3

cot (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

2 x = \frac{π}{6} + πn

2 x = \frac{π}{6} + πn

Solve

2 x = \frac{π}{6} + πn : x = \frac{π}{12} + \frac{πn}{2}

2 x = \frac{π}{6} + πn

Divide both sides by

2

2 x = \frac{π}{6} + πn

Divide both sides by

2

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

Simplify

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

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{π}{6}}{2} + \frac{πn}{2} : \frac{π}{12} + \frac{πn}{2}

\frac{\frac{π}{6}}{2} + \frac{πn}{2}

\frac{\frac{π}{6}}{2} = \frac{π}{12}

\frac{\frac{π}{6}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{6 \cdot 2}

Multiply the numbers:

6 \cdot 2 = 12

= \frac{π}{12}

= \frac{π}{12} + \frac{πn}{2}

x = \frac{π}{12} + \frac{πn}{2}

x = \frac{π}{12} + \frac{πn}{2}

x = \frac{π}{12} + \frac{πn}{2}

x = \frac{π}{12} + \frac{πn}{2}

cot (2 x) = - 3 : x = \frac{5 π}{12} + \frac{πn}{2}

cot (2 x) = - 3

General solutions for

cot (2 x) = - 3

cot (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

2 x = \frac{5 π}{6} + πn

2 x = \frac{5 π}{6} + πn

Solve

2 x = \frac{5 π}{6} + πn : x = \frac{5 π}{12} + \frac{πn}{2}

2 x = \frac{5 π}{6} + πn

Divide both sides by

2

2 x = \frac{5 π}{6} + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{5 π}{6}}{2} + \frac{πn}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{5 π}{6}}{2} + \frac{πn}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{5 π}{6}}{2} + \frac{πn}{2} : \frac{5 π}{12} + \frac{πn}{2}

\frac{\frac{5 π}{6}}{2} + \frac{πn}{2}

\frac{\frac{5 π}{6}}{2} = \frac{5 π}{12}

\frac{\frac{5 π}{6}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{5 π}{6 \cdot 2}

Multiply the numbers:

6 \cdot 2 = 12

= \frac{5 π}{12}

= \frac{5 π}{12} + \frac{πn}{2}

x = \frac{5 π}{12} + \frac{πn}{2}

x = \frac{5 π}{12} + \frac{πn}{2}

x = \frac{5 π}{12} + \frac{πn}{2}

x = \frac{5 π}{12} + \frac{πn}{2}

Combine all the solutions

x = \frac{π}{12} + \frac{πn}{2}, x = \frac{5 π}{12} + \frac{πn}{2}

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Frequently Asked Questions (FAQ)

What is the general solution for 2cot^2(2x)=6 ?
The general solution for 2cot^2(2x)=6 is x= pi/(12)+(pin)/2 ,x=(5pi}{12}+\frac{pin)/2