sin(x-20)+cos(x-20)=0

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Solution for sin(x-20)+cos(x-20)=0 equation:


Simplifying
sin(x + -20) + cos(x + -20) = 0

Reorder the terms:
ins(-20 + x) + cos(x + -20) = 0
(-20 * ins + x * ins) + cos(x + -20) = 0
(-20ins + insx) + cos(x + -20) = 0

Reorder the terms:
-20ins + insx + cos(-20 + x) = 0
-20ins + insx + (-20 * cos + x * cos) = 0
-20ins + insx + (-20cos + cosx) = 0

Reorder the terms:
-20cos + cosx + -20ins + insx = 0

Solving
-20cos + cosx + -20ins + insx = 0

Solving for variable 'c'.

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

Add '20ins' to each side of the equation.
-20cos + cosx + -20ins + 20ins + insx = 0 + 20ins

Combine like terms: -20ins + 20ins = 0
-20cos + cosx + 0 + insx = 0 + 20ins
-20cos + cosx + insx = 0 + 20ins
Remove the zero:
-20cos + cosx + insx = 20ins

Add '-1insx' to each side of the equation.
-20cos + cosx + insx + -1insx = 20ins + -1insx

Combine like terms: insx + -1insx = 0
-20cos + cosx + 0 = 20ins + -1insx
-20cos + cosx = 20ins + -1insx

Reorder the terms:
-20cos + cosx + -20ins + insx = 20ins + -20ins + -1insx + insx

Combine like terms: 20ins + -20ins = 0
-20cos + cosx + -20ins + insx = 0 + -1insx + insx
-20cos + cosx + -20ins + insx = -1insx + insx

Combine like terms: -1insx + insx = 0
-20cos + cosx + -20ins + insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(-20co + cox + -20in + 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 c 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 '(-20co + cox + -20in + inx)' equal to zero and attempt to solve: Simplifying -20co + cox + -20in + inx = 0 Solving -20co + cox + -20in + inx = 0 Move all terms containing c to the left, all other terms to the right. Add '20in' to each side of the equation. -20co + cox + -20in + 20in + inx = 0 + 20in Combine like terms: -20in + 20in = 0 -20co + cox + 0 + inx = 0 + 20in -20co + cox + inx = 0 + 20in Remove the zero: -20co + cox + inx = 20in Add '-1inx' to each side of the equation. -20co + cox + inx + -1inx = 20in + -1inx Combine like terms: inx + -1inx = 0 -20co + cox + 0 = 20in + -1inx -20co + cox = 20in + -1inx 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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