Sine(x-20)=cosine(x)

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Solution for Sine(x-20)=cosine(x) equation:


Simplifying
Sine(x + -20) = cosine(x)

Reorder the terms:
einS(-20 + x) = cosine(x)
(-20 * einS + x * einS) = cosine(x)
(-20einS + einxS) = cosine(x)

Multiply ceinos * x
-20einS + einxS = ceinosx

Solving
-20einS + einxS = ceinosx

Solving for variable 'e'.

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

Add '-1ceinosx' to each side of the equation.
-20einS + -1ceinosx + einxS = ceinosx + -1ceinosx

Reorder the terms:
-1ceinosx + -20einS + einxS = ceinosx + -1ceinosx

Combine like terms: ceinosx + -1ceinosx = 0
-1ceinosx + -20einS + einxS = 0

Factor out the Greatest Common Factor (GCF), 'ein'.
ein(-1cosx + -20S + xS) = 0

Subproblem 1

Set the factor 'ein' equal to zero and attempt to solve: Simplifying ein = 0 Solving ein = 0 Move all terms containing e to the left, all other terms to the right. Simplifying ein = 0 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 '(-1cosx + -20S + xS)' equal to zero and attempt to solve: Simplifying -1cosx + -20S + xS = 0 Reorder the terms: -20S + -1cosx + xS = 0 Solving -20S + -1cosx + xS = 0 Move all terms containing e to the left, all other terms to the right. Add '20S' to each side of the equation. -20S + -1cosx + 20S + xS = 0 + 20S Reorder the terms: -20S + 20S + -1cosx + xS = 0 + 20S Combine like terms: -20S + 20S = 0 0 + -1cosx + xS = 0 + 20S -1cosx + xS = 0 + 20S Remove the zero: -1cosx + xS = 20S Add 'cosx' to each side of the equation. -1cosx + cosx + xS = 20S + cosx Combine like terms: -1cosx + cosx = 0 0 + xS = 20S + cosx xS = 20S + cosx Add '-1xS' to each side of the equation. xS + -1xS = 20S + cosx + -1xS Combine like terms: xS + -1xS = 0 0 = 20S + cosx + -1xS Simplifying 0 = 20S + cosx + -1xS 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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