What is the general solution for cot^2(4x)=3 ?

The general solution for cot^2(4x)=3 is x= pi/(24)+(pin)/4 ,x=(5pi}{24}+\frac{pin)/4

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cot^2(4x)=3

Solution

cot^{2} (4 x) = 3

Solution

x = \frac{π}{24} + \frac{πn}{4}, x = \frac{5 π}{24} + \frac{πn}{4}

Degrees

x = 7. 5^{\circ} + 4 5^{\circ} n, x = 37. 5^{\circ} + 4 5^{\circ} n

Solution steps

cot^{2} (4 x) = 3

Solve by substitution

cot^{2} (4 x) = 3

Let:

cot (4 x) = u

u^{2} = 3

u^{2} = 3 : u = 3, u = - 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 (4 x)

cot (4 x) = 3, cot (4 x) = - 3

cot (4 x) = 3, cot (4 x) = - 3

cot (4 x) = 3 : x = \frac{π}{24} + \frac{πn}{4}

cot (4 x) = 3

General solutions for

cot (4 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

4 x = \frac{π}{6} + πn

4 x = \frac{π}{6} + πn

Solve

4 x = \frac{π}{6} + πn : x = \frac{π}{24} + \frac{πn}{4}

4 x = \frac{π}{6} + πn

Divide both sides by

4

4 x = \frac{π}{6} + πn

Divide both sides by

4

\frac{4 x}{4} = \frac{\frac{π}{6}}{4} + \frac{πn}{4}

Simplify

\frac{4 x}{4} = \frac{\frac{π}{6}}{4} + \frac{πn}{4}

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

\frac{\frac{π}{6}}{4} + \frac{πn}{4} : \frac{π}{24} + \frac{πn}{4}

\frac{\frac{π}{6}}{4} + \frac{πn}{4}

\frac{\frac{π}{6}}{4} = \frac{π}{24}

\frac{\frac{π}{6}}{4}

Apply the fraction rule:

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

= \frac{π}{6 \cdot 4}

Multiply the numbers:

6 \cdot 4 = 24

= \frac{π}{24}

= \frac{π}{24} + \frac{πn}{4}

x = \frac{π}{24} + \frac{πn}{4}

x = \frac{π}{24} + \frac{πn}{4}

x = \frac{π}{24} + \frac{πn}{4}

x = \frac{π}{24} + \frac{πn}{4}

cot (4 x) = - 3 : x = \frac{5 π}{24} + \frac{πn}{4}

cot (4 x) = - 3

General solutions for

cot (4 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

4 x = \frac{5 π}{6} + πn

4 x = \frac{5 π}{6} + πn

Solve

4 x = \frac{5 π}{6} + πn : x = \frac{5 π}{24} + \frac{πn}{4}

4 x = \frac{5 π}{6} + πn

Divide both sides by

4

4 x = \frac{5 π}{6} + πn

Divide both sides by

4

\frac{4 x}{4} = \frac{\frac{5 π}{6}}{4} + \frac{πn}{4}

Simplify

\frac{4 x}{4} = \frac{\frac{5 π}{6}}{4} + \frac{πn}{4}

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

\frac{\frac{5 π}{6}}{4} + \frac{πn}{4} : \frac{5 π}{24} + \frac{πn}{4}

\frac{\frac{5 π}{6}}{4} + \frac{πn}{4}

\frac{\frac{5 π}{6}}{4} = \frac{5 π}{24}

\frac{\frac{5 π}{6}}{4}

Apply the fraction rule:

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

= \frac{5 π}{6 \cdot 4}

Multiply the numbers:

6 \cdot 4 = 24

= \frac{5 π}{24}

= \frac{5 π}{24} + \frac{πn}{4}

x = \frac{5 π}{24} + \frac{πn}{4}

x = \frac{5 π}{24} + \frac{πn}{4}

x = \frac{5 π}{24} + \frac{πn}{4}

x = \frac{5 π}{24} + \frac{πn}{4}

Combine all the solutions

x = \frac{π}{24} + \frac{πn}{4}, x = \frac{5 π}{24} + \frac{πn}{4}

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Frequently Asked Questions (FAQ)

What is the general solution for cot^2(4x)=3 ?
The general solution for cot^2(4x)=3 is x= pi/(24)+(pin)/4 ,x=(5pi}{24}+\frac{pin)/4