What is the general solution for cot^5(x)=(-1)/((sqrt(3))) ?

The general solution for cot^5(x)=(-1)/((sqrt(3))) is x=2.30137…+pin

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cot^5(x)=(-1)/((sqrt(3)))

cot^{5} (x) = \frac{- 1}{( 3 )}

x = 2.30137 \dots + πn

Solution steps

cot^{5} (x) = \frac{- 1}{( 3 )}

Simplify

\frac{- 1}{3} : - \frac{3}{3}

\frac{- 1}{3}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1}{3}

Rationalize

- \frac{1}{3} : - \frac{3}{3}

- \frac{1}{3}

Multiply by the conjugate

\frac{3}{3}

= - \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= - \frac{3}{3}

= - \frac{3}{3}

cot^{5} (x) = - \frac{3}{3}

For

x^{n} = f (a)

, n is odd, the solution is

Apply radical rule:

n

is odd

Apply trig inverse properties

General solutions for

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

Show solutions in decimal form

x = 2.30137 \dots + πn

2 cos^{4} (x) cos (x) - cos^{5} (x) = 1

cos^{4} (x) - 2 sin^{2} (x) - 1 = 0

d^{2} (1 + cos (x)) - (1 + cos (x))^{2} = sin^{2} (x)

cos^{4} (x) - 2 cos^{2} (x) + 1 = 0

sin^{2} (x) + cos^{2} (x) + cos (x) = 2

What is the general solution for cot^5(x)=(-1)/((sqrt(3))) ?
The general solution for cot^5(x)=(-1)/((sqrt(3))) is x=2.30137…+pin