Cos(3x-30)-Sin(3x-60)=0

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Solution for Cos(3x-30)-Sin(3x-60)=0 equation: 


Simplifying
Cos(3x + -30) + -1Sin(3x + -60) = 0

Reorder the terms:
osC(-30 + 3x) + -1Sin(3x + -60) = 0
(-30 * osC + 3x * osC) + -1Sin(3x + -60) = 0
(-30osC + 3osxC) + -1Sin(3x + -60) = 0

Reorder the terms:
-30osC + 3osxC + -1inS(-60 + 3x) = 0
-30osC + 3osxC + (-60 * -1inS + 3x * -1inS) = 0
-30osC + 3osxC + (60inS + -3inxS) = 0

Reorder the terms:
60inS + -3inxS + -30osC + 3osxC = 0

Solving
60inS + -3inxS + -30osC + 3osxC = 0

Solving for variable 'i'.

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

Add '30osC' to each side of the equation.
60inS + -3inxS + -30osC + 30osC + 3osxC = 0 + 30osC

Combine like terms: -30osC + 30osC = 0
60inS + -3inxS + 0 + 3osxC = 0 + 30osC
60inS + -3inxS + 3osxC = 0 + 30osC
Remove the zero:
60inS + -3inxS + 3osxC = 30osC

Add '-3osxC' to each side of the equation.
60inS + -3inxS + 3osxC + -3osxC = 30osC + -3osxC

Combine like terms: 3osxC + -3osxC = 0
60inS + -3inxS + 0 = 30osC + -3osxC
60inS + -3inxS = 30osC + -3osxC

Reorder the terms:
60inS + -3inxS + -30osC + 3osxC = 30osC + -30osC + -3osxC + 3osxC

Combine like terms: 30osC + -30osC = 0
60inS + -3inxS + -30osC + 3osxC = 0 + -3osxC + 3osxC
60inS + -3inxS + -30osC + 3osxC = -3osxC + 3osxC

Combine like terms: -3osxC + 3osxC = 0
60inS + -3inxS + -30osC + 3osxC = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(20inS + -1inxS + -10osC + osxC) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(20inS + -1inxS + -10osC + osxC)' equal to zero and attempt to solve:

Simplifying
20inS + -1inxS + -10osC + osxC = 0

Solving
20inS + -1inxS + -10osC + osxC = 0

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

Add '10osC' to each side of the equation.
20inS + -1inxS + -10osC + 10osC + osxC = 0 + 10osC

Combine like terms: -10osC + 10osC = 0
20inS + -1inxS + 0 + osxC = 0 + 10osC
20inS + -1inxS + osxC = 0 + 10osC
Remove the zero:
20inS + -1inxS + osxC = 10osC

Add '-1osxC' to each side of the equation.
20inS + -1inxS + osxC + -1osxC = 10osC + -1osxC

Combine like terms: osxC + -1osxC = 0
20inS + -1inxS + 0 = 10osC + -1osxC
20inS + -1inxS = 10osC + -1osxC

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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