Sin(x-pi)=-sinx

Solution for Sin(x-pi)=-sinx equation:

Simplifying
Sin(x + -1pi) = -1sinx

Reorder the terms:
inS(-1ip + x) = -1sinx
(-1ip * inS + x * inS) = -1sinx

Reorder the terms:
(inxS + -1i2npS) = -1sinx
(inxS + -1i2npS) = -1sinx

Solving
inxS + -1i2npS = -1insx

Solving for variable 'i'.

Reorder the terms:
insx + inxS + -1i2npS = -1insx + insx

Combine like terms: -1insx + insx = 0
insx + inxS + -1i2npS = 0

Factor out the Greatest Common Factor (GCF), 'in'.
in(sx + xS + -1ipS) = 0

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

Simplifying
in = 0

Solving
in = 0

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

Simplifying
in = 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 '(sx + xS + -1ipS)' equal to zero and attempt to solve:

Simplifying
sx + xS + -1ipS = 0

Reorder the terms:
-1ipS + sx + xS = 0

Solving
-1ipS + sx + xS = 0

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

Add '-1sx' to each side of the equation.
-1ipS + sx + -1sx + xS = 0 + -1sx

Combine like terms: sx + -1sx = 0
-1ipS + 0 + xS = 0 + -1sx
-1ipS + xS = 0 + -1sx
Remove the zero:
-1ipS + xS = -1sx

Add '-1xS' to each side of the equation.
-1ipS + xS + -1xS = -1sx + -1xS

Combine like terms: xS + -1xS = 0
-1ipS + 0 = -1sx + -1xS
-1ipS = -1sx + -1xS

Divide each side by '-1pS'.
i = p-1sxS-1 + p-1x

Simplifying
i = p-1sxS-1 + p-1x
Solution
i = {p-1sxS-1 + p-1x}