What is the general solution for 4arccos(2x)=pi ?

The general solution for 4arccos(2x)=pi is x= 1/(2sqrt(2))

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4arccos(2x)=pi

4 arccos (2 x) = π

x = \frac{1}{2 2}

Solution steps

4 arccos (2 x) = π

Divide both sides by

4

4 arccos (2 x) = π

Divide both sides by

4

\frac{4 arccos ( 2 x )}{4} = \frac{π}{4}

Simplify

arccos (2 x) = \frac{π}{4}

arccos (2 x) = \frac{π}{4}

Apply trig inverse properties

arccos (2 x) = \frac{π}{4}

arccos (x) = a \Rightarrow x = cos (a)

2 x = cos (\frac{π}{4})

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{π}{4})

cos (x)

periodicity table with

2 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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

= \frac{2}{2}

2 x = \frac{2}{2}

2 x = \frac{2}{2}

Solve

2 x = \frac{2}{2} : x = \frac{1}{2 2}

2 x = \frac{2}{2}

Apply radical rule:

a = a a

2 = 22

2 x = \frac{2}{2 2}

Cancel the common factor:

2

2 x = \frac{1}{2}

Divide both sides by

2

2 x = \frac{1}{2}

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{1}{2}}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{1}{2}}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Cancel the common factor:

2

= x

Simplify

\frac{\frac{1}{2}}{2} : \frac{1}{2 2}

\frac{\frac{1}{2}}{2}

Apply the fraction rule:

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

= \frac{1}{2 \cdot 2}

= \frac{1}{2 2}

x = \frac{1}{2 2}

x = \frac{1}{2 2}

x = \frac{1}{2 2}

x = \frac{1}{2 2}

tan (x) = 2 - 1

5 + 3 cos (\frac{1}{2} x) = 7

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

sin (2 x - 0.35) = cos (3 x)

2 cos^{2} (x) - 15 cos (x) + 7 = 0

What is the general solution for 4arccos(2x)=pi ?
The general solution for 4arccos(2x)=pi is x= 1/(2sqrt(2))