Question

Solve 3cosx = 2+cosx​

Answer 1

x= 0.

Explanation:

1. Write the expression.

`3cosx = 2+cosx`

2. Divide both sides by 3.

`(3cosx)/(3) = (2+cosx)/(3) \\\\(3cosx)/(3) = (2)/(3) +(cosx)/(3) \\ \\cosx=(2)/(3) +(cosx)/(3)`

3. Subtract
`(cosx)/(3)` from both sides.

`(3cosx)/(3) = (2+cosx)/(3) \\\\(3cosx)/(3) = (2)/(3) +(cosx)/(3) \\ \\cosx-(cosx)/(3)=(2)/(3) +(cosx)/(3)-(cosx)/(3)\\ \\\\cosx-(cosx)/(3)=(2)/(3)`

4. Simplify the fraction subtraction.

`(3cosx)/(3) -(cosx)/(3)=(2)/(3)\\ \\(3cosx-cosx)/(3)=(2)/(3)`

5. Multiply both sides by 3.

`3*(3cosx-cosx)/(3)=(2)/(3)*3\\ \\3cosx-cosx=(6)/(3)\\ \\3cosx-cosx=2`

6. Solve the subtraction.

`2cosx=2`

7. Divide both sides by 2.

`(2cosx)/(2) =(2)/(2) \\ \\cosx=1`

8. Take
`cos^(-1)` from both sides.

`cos^(-1)(cosx) =cos^(-1)(1)\\ \\x=cos^(-1)(1)\\ \\x=0.`