Sin[2x-30]=Cos[4x-60]

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Solution for Sin[2x-30]=Cos[4x-60] equation: 


Simplifying
Sin[2x + -30] = Cos[4x + -60]

Reorder the terms:
inS[-30 + 2x] = Cos[4x + -60]
[-30 * inS + 2x * inS] = Cos[4x + -60]
[-30inS + 2inxS] = Cos[4x + -60]

Reorder the terms:
-30inS + 2inxS = osC[-60 + 4x]
-30inS + 2inxS = [-60 * osC + 4x * osC]
-30inS + 2inxS = [-60osC + 4osxC]

Solving
-30inS + 2inxS = -60osC + 4osxC

Solving for variable 'i'.

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

Reorder the terms:
-30inS + 2inxS + 60osC + -4osxC = -60osC + 60osC + 4osxC + -4osxC

Combine like terms: -60osC + 60osC = 0
-30inS + 2inxS + 60osC + -4osxC = 0 + 4osxC + -4osxC
-30inS + 2inxS + 60osC + -4osxC = 4osxC + -4osxC

Combine like terms: 4osxC + -4osxC = 0
-30inS + 2inxS + 60osC + -4osxC = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15inS + inxS + 30osC + -2osxC) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15inS + inxS + 30osC + -2osxC)' equal to zero and attempt to solve:

Simplifying
-15inS + inxS + 30osC + -2osxC = 0

Solving
-15inS + inxS + 30osC + -2osxC = 0

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

Add '-30osC' to each side of the equation.
-15inS + inxS + 30osC + -30osC + -2osxC = 0 + -30osC

Combine like terms: 30osC + -30osC = 0
-15inS + inxS + 0 + -2osxC = 0 + -30osC
-15inS + inxS + -2osxC = 0 + -30osC
Remove the zero:
-15inS + inxS + -2osxC = -30osC

Add '2osxC' to each side of the equation.
-15inS + inxS + -2osxC + 2osxC = -30osC + 2osxC

Combine like terms: -2osxC + 2osxC = 0
-15inS + inxS + 0 = -30osC + 2osxC
-15inS + inxS = -30osC + 2osxC

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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