sin(3x+25)=cos(2x+10)

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Solution for sin(3x+25)=cos(2x+10) equation:


Simplifying
sin(3x + 25) = cos(2x + 10)

Reorder the terms:
ins(25 + 3x) = cos(2x + 10)
(25 * ins + 3x * ins) = cos(2x + 10)
(25ins + 3insx) = cos(2x + 10)

Reorder the terms:
25ins + 3insx = cos(10 + 2x)
25ins + 3insx = (10 * cos + 2x * cos)
25ins + 3insx = (10cos + 2cosx)

Solving
25ins + 3insx = 10cos + 2cosx

Solving for variable 'i'.

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

Reorder the terms:
-10cos + -2cosx + 25ins + 3insx = 10cos + 2cosx + -10cos + -2cosx

Reorder the terms:
-10cos + -2cosx + 25ins + 3insx = 10cos + -10cos + 2cosx + -2cosx

Combine like terms: 10cos + -10cos = 0
-10cos + -2cosx + 25ins + 3insx = 0 + 2cosx + -2cosx
-10cos + -2cosx + 25ins + 3insx = 2cosx + -2cosx

Combine like terms: 2cosx + -2cosx = 0
-10cos + -2cosx + 25ins + 3insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(-10co + -2cox + 25in + 3inx) = 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 '(-10co + -2cox + 25in + 3inx)' equal to zero and attempt to solve: Simplifying -10co + -2cox + 25in + 3inx = 0 Solving -10co + -2cox + 25in + 3inx = 0 Move all terms containing i to the left, all other terms to the right. Add '10co' to each side of the equation. -10co + -2cox + 25in + 10co + 3inx = 0 + 10co Reorder the terms: -10co + 10co + -2cox + 25in + 3inx = 0 + 10co Combine like terms: -10co + 10co = 0 0 + -2cox + 25in + 3inx = 0 + 10co -2cox + 25in + 3inx = 0 + 10co Remove the zero: -2cox + 25in + 3inx = 10co Add '2cox' to each side of the equation. -2cox + 25in + 2cox + 3inx = 10co + 2cox Reorder the terms: -2cox + 2cox + 25in + 3inx = 10co + 2cox Combine like terms: -2cox + 2cox = 0 0 + 25in + 3inx = 10co + 2cox 25in + 3inx = 10co + 2cox 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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