sin(x+45)=5cos(x-45)

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Solution for sin(x+45)=5cos(x-45) equation: 


Simplifying
sin(x + 45) = 5cos(x + -45)

Reorder the terms:
ins(45 + x) = 5cos(x + -45)
(45 * ins + x * ins) = 5cos(x + -45)
(45ins + insx) = 5cos(x + -45)

Reorder the terms:
45ins + insx = 5cos(-45 + x)
45ins + insx = (-45 * 5cos + x * 5cos)
45ins + insx = (-225cos + 5cosx)

Solving
45ins + insx = -225cos + 5cosx

Solving for variable 'i'.

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

Reorder the terms:
225cos + -5cosx + 45ins + insx = -225cos + 5cosx + 225cos + -5cosx

Reorder the terms:
225cos + -5cosx + 45ins + insx = -225cos + 225cos + 5cosx + -5cosx

Combine like terms: -225cos + 225cos = 0
225cos + -5cosx + 45ins + insx = 0 + 5cosx + -5cosx
225cos + -5cosx + 45ins + insx = 5cosx + -5cosx

Combine like terms: 5cosx + -5cosx = 0
225cos + -5cosx + 45ins + insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(225co + -5cox + 45in + inx) = 0


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

Simplifying
s = 0

Solving
s = 0

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

Add '-1s' to each side of the equation.
s + -1s = 0 + -1s
Remove the zero:
0 = -1s

Simplifying
0 = -1s

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 '(225co + -5cox + 45in + inx)' equal to zero and attempt to solve:

Simplifying
225co + -5cox + 45in + inx = 0

Solving
225co + -5cox + 45in + inx = 0

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

Add '-225co' to each side of the equation.
225co + -5cox + 45in + -225co + inx = 0 + -225co

Reorder the terms:
225co + -225co + -5cox + 45in + inx = 0 + -225co

Combine like terms: 225co + -225co = 0
0 + -5cox + 45in + inx = 0 + -225co
-5cox + 45in + inx = 0 + -225co
Remove the zero:
-5cox + 45in + inx = -225co

Add '5cox' to each side of the equation.
-5cox + 45in + 5cox + inx = -225co + 5cox

Reorder the terms:
-5cox + 5cox + 45in + inx = -225co + 5cox

Combine like terms: -5cox + 5cox = 0
0 + 45in + inx = -225co + 5cox
45in + inx = -225co + 5cox

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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