What is the general solution for arccosh(x)=(2pi)/5 ?

The general solution for arccosh(x)=(2pi)/5 is No Solution for x\in\mathbb{R}

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arccosh(x)=(2pi)/5

arccosh (x) = \frac{2 π}{5}

No Solution for x \in R

Solution steps

arccosh (x) = \frac{2 π}{5}

Subtract

\frac{2 π}{5}

from both sides

arccosh (x) - \frac{2 π}{5} = 0

Simplify

arccosh (x) - \frac{2 π}{5} : \frac{5 arccosh ( x ) - 2 π}{5}

\frac{5 arccosh ( x ) - 2 π}{5} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

5 arccosh (x) - 2 π = 0

Solve by substitution

arccosh (x) = \frac{2 π}{5}

Rewrite using trig identities

- 2 π + 5 ln (- 1 + x^{2} + x) = 0

Move

2 π

to the right side

5 ln (- 1 + x^{2} + x) = 2 π

Divide both sides by

5

ln (- 1 + x^{2} + x) = \frac{2 π}{5}

Apply trig inverse properties

Solve

No Solution for

x \in R

Solve

No Solution for

x \in R

No Solution for x \in R

- 6 sin (x) - 4 sin (2 x) = 0

t, x = 2 cos (t)

6 sin (θ) = 2.5 cos (θ)

tan^{3} (x) + tan^{2} (x) - tan (x) - 1 = 0

tan (θ) = \frac{- 4 3}{4}

What is the general solution for arccosh(x)=(2pi)/5 ?
The general solution for arccosh(x)=(2pi)/5 is No Solution for x\in\mathbb{R}