sin(x)+2cos(4x)=sqrt(3)cos(x)

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Solution for sin(x)+2cos(4x)=sqrt(3)cos(x) equation: 


Simplifying
sin(x) + 2cos(4x) = sqrt(3) * cos(x)

Multiply ins * x
insx + 2cos(4x) = sqrt(3) * cos(x)

Remove parenthesis around (4x)
insx + 2cos * 4x = sqrt(3) * cos(x)

Reorder the terms for easier multiplication:
insx + 2 * 4cos * x = sqrt(3) * cos(x)

Multiply 2 * 4
insx + 8cos * x = sqrt(3) * cos(x)

Multiply cos * x
insx + 8cosx = sqrt(3) * cos(x)

Reorder the terms:
8cosx + insx = sqrt(3) * cos(x)

Reorder the terms for easier multiplication:
8cosx + insx = 3qrst * cos * x

Multiply qrst * cos
8cosx + insx = 3coqrs2t * x

Multiply coqrs2t * x
8cosx + insx = 3coqrs2tx

Solving
8cosx + insx = 3coqrs2tx

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '-3coqrs2tx' to each side of the equation.
8cosx + -3coqrs2tx + insx = 3coqrs2tx + -3coqrs2tx

Reorder the terms:
-3coqrs2tx + 8cosx + insx = 3coqrs2tx + -3coqrs2tx

Combine like terms: 3coqrs2tx + -3coqrs2tx = 0
-3coqrs2tx + 8cosx + insx = 0

Add '-1insx' to each side of the equation.
-3coqrs2tx + 8cosx + insx + -1insx = 0 + -1insx

Combine like terms: insx + -1insx = 0
-3coqrs2tx + 8cosx + 0 = 0 + -1insx
-3coqrs2tx + 8cosx = 0 + -1insx
Remove the zero:
-3coqrs2tx + 8cosx = -1insx

Combine like terms: -1insx + insx = 0
-3coqrs2tx + 8cosx + insx = 0

Factor out the Greatest Common Factor (GCF), 'sx'.
sx(-3coqrst + 8co + in) = 0


Subproblem 1
Set the factor 'sx' equal to zero and attempt to solve:

Simplifying
sx = 0

Solving
sx = 0

Move all terms containing c to the left, all other terms to the right.

Add '-1sx' to each side of the equation.
sx + -1sx = 0 + -1sx
Remove the zero:
0 = -1sx

Simplifying
0 = -1sx

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-3coqrst + 8co + in)' equal to zero and attempt to solve:

Simplifying
-3coqrst + 8co + in = 0

Reorder the terms:
8co + -3coqrst + in = 0

Solving
8co + -3coqrst + in = 0

Move all terms containing c to the left, all other terms to the right.

Add '-1in' to each side of the equation.
8co + -3coqrst + in + -1in = 0 + -1in

Combine like terms: in + -1in = 0
8co + -3coqrst + 0 = 0 + -1in
8co + -3coqrst = 0 + -1in
Remove the zero:
8co + -3coqrst = -1in

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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