What is the general solution for sqrt(5)cot(x/2)=sqrt(5) ?

The general solution for sqrt(5)cot(x/2)=sqrt(5) is x= pi/2+2pin

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sqrt(5)cot(x/2)=sqrt(5)

5 cot (\frac{x}{2}) = 5

x = \frac{π}{2} + 2 πn

Degrees

x = 9 0^{\circ} + 36 0^{\circ} n

Solution steps

5 cot (\frac{x}{2}) = 5

Divide both sides by

5

5 cot (\frac{x}{2}) = 5

Divide both sides by

5

\frac{5 cot ( \frac{x}{2} )}{5} = \frac{5}{5}

Simplify

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

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

General solutions for

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

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

\frac{x}{2} = \frac{π}{4} + πn

\frac{x}{2} = \frac{π}{4} + πn

Solve

\frac{x}{2} = \frac{π}{4} + πn : x = \frac{π}{2} + 2 πn

\frac{x}{2} = \frac{π}{4} + πn

Multiply both sides by

2

\frac{x}{2} = \frac{π}{4} + πn

Multiply both sides by

2

\frac{2 x}{2} = 2 \cdot \frac{π}{4} + 2 πn

Simplify

\frac{2 x}{2} = 2 \cdot \frac{π}{4} + 2 πn

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

2 \cdot \frac{π}{4} + 2 πn : \frac{π}{2} + 2 πn

2 \cdot \frac{π}{4} + 2 πn

2 \cdot \frac{π}{4} = \frac{π}{2}

2 \cdot \frac{π}{4}

Multiply fractions:

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

= \frac{π 2}{4}

Cancel the common factor:

2

= \frac{π}{2}

= \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

tan (θ) = \frac{8}{7}

1 - cos (x) = sin (x)

tan (x) = \frac{15}{8}

tan^{2} (x) + 3 sec (x) + 3 = 0

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

What is the general solution for sqrt(5)cot(x/2)=sqrt(5) ?
The general solution for sqrt(5)cot(x/2)=sqrt(5) is x= pi/2+2pin