Cos(x+10)=sin(x-20)

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Solution for Cos(x+10)=sin(x-20) equation:


Simplifying
Cos(x + 10) = sin(x + -20)

Reorder the terms:
osC(10 + x) = sin(x + -20)
(10 * osC + x * osC) = sin(x + -20)
(10osC + osxC) = sin(x + -20)

Reorder the terms:
10osC + osxC = ins(-20 + x)
10osC + osxC = (-20 * ins + x * ins)
10osC + osxC = (-20ins + insx)

Solving
10osC + osxC = -20ins + insx

Solving for variable 'o'.

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

Reorder the terms:
20ins + -1insx + 10osC + osxC = -20ins + insx + 20ins + -1insx

Reorder the terms:
20ins + -1insx + 10osC + osxC = -20ins + 20ins + insx + -1insx

Combine like terms: -20ins + 20ins = 0
20ins + -1insx + 10osC + osxC = 0 + insx + -1insx
20ins + -1insx + 10osC + osxC = insx + -1insx

Combine like terms: insx + -1insx = 0
20ins + -1insx + 10osC + osxC = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(20in + -1inx + 10oC + oxC) = 0

Subproblem 1

Set the factor 's' equal to zero and attempt to solve: Simplifying s = 0 Solving s = 0 Move all terms containing o 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 '(20in + -1inx + 10oC + oxC)' equal to zero and attempt to solve: Simplifying 20in + -1inx + 10oC + oxC = 0 Solving 20in + -1inx + 10oC + oxC = 0 Move all terms containing o to the left, all other terms to the right. Add '-20in' to each side of the equation. 20in + -1inx + 10oC + -20in + oxC = 0 + -20in Reorder the terms: 20in + -20in + -1inx + 10oC + oxC = 0 + -20in Combine like terms: 20in + -20in = 0 0 + -1inx + 10oC + oxC = 0 + -20in -1inx + 10oC + oxC = 0 + -20in Remove the zero: -1inx + 10oC + oxC = -20in Add 'inx' to each side of the equation. -1inx + 10oC + inx + oxC = -20in + inx Reorder the terms: -1inx + inx + 10oC + oxC = -20in + inx Combine like terms: -1inx + inx = 0 0 + 10oC + oxC = -20in + inx 10oC + oxC = -20in + inx 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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