What is the general solution for 4cos(x)+6=5(cos(x)+1) ?

The general solution for 4cos(x)+6=5(cos(x)+1) is x=2pin

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Popular >

4cos(x)+6=5(cos(x)+1)

Solution

4 cos (x) + 6 = 5 (cos (x) + 1)

Solution

x = 2 πn

Degrees

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

Solution steps

4 cos (x) + 6 = 5 (cos (x) + 1)

Solve by substitution

4 cos (x) + 6 = 5 (cos (x) + 1)

Let:

cos (x) = u

4 u + 6 = 5 (u + 1)

4 u + 6 = 5 (u + 1) : u = 1

4 u + 6 = 5 (u + 1)

Expand

5 (u + 1) : 5 u + 5

5 (u + 1)

Apply the distributive law:

a (b + c) = ab + a c

a = 5, b = u, c = 1

= 5 u + 5 \cdot 1

Multiply the numbers:

5 \cdot 1 = 5

= 5 u + 5

4 u + 6 = 5 u + 5

Move

6

to the right side

4 u + 6 = 5 u + 5

Subtract

6

from both sides

4 u + 6 - 6 = 5 u + 5 - 6

Simplify

4 u = 5 u - 1

4 u = 5 u - 1

Move

5 u

to the left side

4 u = 5 u - 1

Subtract

5 u

from both sides

4 u - 5 u = 5 u - 1 - 5 u

Simplify

- u = - 1

- u = - 1

Divide both sides by

- 1

- u = - 1

Divide both sides by

- 1

\frac{- u}{- 1} = \frac{- 1}{- 1}

Simplify

u = 1

u = 1

Substitute back

u = cos (x)

cos (x) = 1

cos (x) = 1

cos (x) = 1 : x = 2 πn

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

Combine all the solutions

x = 2 πn

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Frequently Asked Questions (FAQ)

What is the general solution for 4cos(x)+6=5(cos(x)+1) ?
The general solution for 4cos(x)+6=5(cos(x)+1) is x=2pin