3cos(x+40)=4sin(x+40)

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Solution for 3cos(x+40)=4sin(x+40) equation: 


Simplifying
3cos(x + 40) = 4sin(x + 40)

Reorder the terms:
3cos(40 + x) = 4sin(x + 40)
(40 * 3cos + x * 3cos) = 4sin(x + 40)
(120cos + 3cosx) = 4sin(x + 40)

Reorder the terms:
120cos + 3cosx = 4ins(40 + x)
120cos + 3cosx = (40 * 4ins + x * 4ins)
120cos + 3cosx = (160ins + 4insx)

Solving
120cos + 3cosx = 160ins + 4insx

Solving for variable 'c'.

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

Reorder the terms:
120cos + 3cosx + -160ins + -4insx = 160ins + -160ins + 4insx + -4insx

Combine like terms: 160ins + -160ins = 0
120cos + 3cosx + -160ins + -4insx = 0 + 4insx + -4insx
120cos + 3cosx + -160ins + -4insx = 4insx + -4insx

Combine like terms: 4insx + -4insx = 0
120cos + 3cosx + -160ins + -4insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(120co + 3cox + -160in + -4inx) = 0


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

Simplifying
s = 0

Solving
s = 0

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

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

Simplifying
0 = -1s

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 '(120co + 3cox + -160in + -4inx)' equal to zero and attempt to solve:

Simplifying
120co + 3cox + -160in + -4inx = 0

Solving
120co + 3cox + -160in + -4inx = 0

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

Add '160in' to each side of the equation.
120co + 3cox + -160in + 160in + -4inx = 0 + 160in

Combine like terms: -160in + 160in = 0
120co + 3cox + 0 + -4inx = 0 + 160in
120co + 3cox + -4inx = 0 + 160in
Remove the zero:
120co + 3cox + -4inx = 160in

Add '4inx' to each side of the equation.
120co + 3cox + -4inx + 4inx = 160in + 4inx

Combine like terms: -4inx + 4inx = 0
120co + 3cox + 0 = 160in + 4inx
120co + 3cox = 160in + 4inx

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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