What is the general solution for 4cos(x)-3cos(x)-1=0 ?

The general solution for 4cos(x)-3cos(x)-1=0 is x=2pin

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4cos(x)-3cos(x)-1=0

4 cos (x) - 3 cos (x) - 1 = 0

x = 2 πn

Degrees

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

Solution steps

4 cos (x) - 3 cos (x) - 1 = 0

Simplify

4 cos (x) - 3 cos (x) - 1 : cos (x) - 1

4 cos (x) - 3 cos (x) - 1

Add similar elements:

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

= cos (x) - 1

cos (x) - 1 = 0

Move

1

to the right side

cos (x) - 1 = 0

Add

1

to both sides

cos (x) - 1 + 1 = 0 + 1

Simplify

cos (x) = 1

cos (x) = 1

General solutions for

cos (x) = 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 = 0 + 2 πn

x = 0 + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

What is the general solution for 4cos(x)-3cos(x)-1=0 ?
The general solution for 4cos(x)-3cos(x)-1=0 is x=2pin