What is the general solution for 4cos(x-pi)=4 ?

The general solution for 4cos(x-pi)=4 is x=2pin+pi

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4cos(x-pi)=4

4 cos (x - π) = 4

x = 2 πn + π

Degrees

x = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

4 cos (x - π) = 4

Divide both sides by

4

4 cos (x - π) = 4

Divide both sides by

4

\frac{4 cos ( x - π )}{4} = \frac{4}{4}

Simplify

cos (x - π) = 1

cos (x - π) = 1

General solutions for

cos (x - π) = 1

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}

x - π = 0 + 2 πn

x - π = 0 + 2 πn

Solve

x - π = 0 + 2 πn : x = 2 πn + π

x - π = 0 + 2 πn

0 + 2 πn = 2 πn

x - π = 2 πn

Move

π

to the right side

x - π = 2 πn

Add

π

to both sides

x - π + π = 2 πn + π

Simplify

x = 2 πn + π

x = 2 πn + π

x = 2 πn + π

cot (x) (tan (x) - \frac{3}{3}) = 0

3 = sec (x)

2 cos (2 x) = 1

2 csc^{2} (x) = 1 + cos (x)

6 arccos (5 x) = 5 π

What is the general solution for 4cos(x-pi)=4 ?
The general solution for 4cos(x-pi)=4 is x=2pin+pi