sine(3x+50)-cosine(2x-10)=0

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Solution for sine(3x+50)-cosine(2x-10)=0 equation:


Simplifying
sine(3x + 50) + -1cosine(2x + -10) = 0

Reorder the terms:
eins(50 + 3x) + -1cosine(2x + -10) = 0
(50 * eins + 3x * eins) + -1cosine(2x + -10) = 0
(50eins + 3einsx) + -1cosine(2x + -10) = 0

Reorder the terms:
50eins + 3einsx + -1ceinos(-10 + 2x) = 0
50eins + 3einsx + (-10 * -1ceinos + 2x * -1ceinos) = 0
50eins + 3einsx + (10ceinos + -2ceinosx) = 0

Reorder the terms:
10ceinos + -2ceinosx + 50eins + 3einsx = 0

Solving
10ceinos + -2ceinosx + 50eins + 3einsx = 0

Solving for variable 'c'.

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

Add '-50eins' to each side of the equation.
10ceinos + -2ceinosx + 50eins + -50eins + 3einsx = 0 + -50eins

Combine like terms: 50eins + -50eins = 0
10ceinos + -2ceinosx + 0 + 3einsx = 0 + -50eins
10ceinos + -2ceinosx + 3einsx = 0 + -50eins
Remove the zero:
10ceinos + -2ceinosx + 3einsx = -50eins

Add '-3einsx' to each side of the equation.
10ceinos + -2ceinosx + 3einsx + -3einsx = -50eins + -3einsx

Combine like terms: 3einsx + -3einsx = 0
10ceinos + -2ceinosx + 0 = -50eins + -3einsx
10ceinos + -2ceinosx = -50eins + -3einsx

Reorder the terms:
10ceinos + -2ceinosx + 50eins + 3einsx = -50eins + 50eins + -3einsx + 3einsx

Combine like terms: -50eins + 50eins = 0
10ceinos + -2ceinosx + 50eins + 3einsx = 0 + -3einsx + 3einsx
10ceinos + -2ceinosx + 50eins + 3einsx = -3einsx + 3einsx

Combine like terms: -3einsx + 3einsx = 0
10ceinos + -2ceinosx + 50eins + 3einsx = 0

Factor out the Greatest Common Factor (GCF), 'eins'.
eins(10co + -2cox + 50 + 3x) = 0

Subproblem 1

Set the factor 'eins' equal to zero and attempt to solve: Simplifying eins = 0 Solving eins = 0 Move all terms containing c to the left, all other terms to the right. Add '-1eins' to each side of the equation. eins + -1eins = 0 + -1eins Remove the zero: 0 = -1eins Simplifying 0 = -1eins 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 '(10co + -2cox + 50 + 3x)' equal to zero and attempt to solve: Simplifying 10co + -2cox + 50 + 3x = 0 Reorder the terms: 50 + 10co + -2cox + 3x = 0 Solving 50 + 10co + -2cox + 3x = 0 Move all terms containing c to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + 10co + -2cox + -50 + 3x = 0 + -50 Reorder the terms: 50 + -50 + 10co + -2cox + 3x = 0 + -50 Combine like terms: 50 + -50 = 0 0 + 10co + -2cox + 3x = 0 + -50 10co + -2cox + 3x = 0 + -50 Combine like terms: 0 + -50 = -50 10co + -2cox + 3x = -50 Add '-3x' to each side of the equation. 10co + -2cox + 3x + -3x = -50 + -3x Combine like terms: 3x + -3x = 0 10co + -2cox + 0 = -50 + -3x 10co + -2cox = -50 + -3x 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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