(cosx-sinx)(cosx+sinx)=cos(2x)

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Solution for (cosx-sinx)(cosx+sinx)=cos(2x) equation: 


Simplifying
(cosx + -1sinx)(cosx + sinx) = cos(2x)

Multiply (cosx + -1insx) * (cosx + insx)
(cosx(cosx + insx) + -1insx * (cosx + insx)) = cos(2x)
((cosx * cosx + insx * cosx) + -1insx * (cosx + insx)) = cos(2x)

Reorder the terms:
((cinos2x2 + c2o2s2x2) + -1insx * (cosx + insx)) = cos(2x)
((cinos2x2 + c2o2s2x2) + -1insx * (cosx + insx)) = cos(2x)
(cinos2x2 + c2o2s2x2 + (cosx * -1insx + insx * -1insx)) = cos(2x)
(cinos2x2 + c2o2s2x2 + (-1cinos2x2 + -1i2n2s2x2)) = cos(2x)

Reorder the terms:
(cinos2x2 + -1cinos2x2 + c2o2s2x2 + -1i2n2s2x2) = cos(2x)

Combine like terms: cinos2x2 + -1cinos2x2 = 0
(0 + c2o2s2x2 + -1i2n2s2x2) = cos(2x)
(c2o2s2x2 + -1i2n2s2x2) = cos(2x)

Remove parenthesis around (2x)
c2o2s2x2 + -1i2n2s2x2 = cos * 2x

Reorder the terms for easier multiplication:
c2o2s2x2 + -1i2n2s2x2 = 2cos * x

Multiply cos * x
c2o2s2x2 + -1i2n2s2x2 = 2cosx

Solving
c2o2s2x2 + -1i2n2s2x2 = 2cosx

Solving for variable 'c'.

Reorder the terms:
-2cosx + c2o2s2x2 + -1i2n2s2x2 = 2cosx + -2cosx

Combine like terms: 2cosx + -2cosx = 0
-2cosx + c2o2s2x2 + -1i2n2s2x2 = 0

Factor out the Greatest Common Factor (GCF), 'sx'.
sx(-2co + c2o2sx + -1i2n2sx) = 0


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

Simplifying
sx = 0

Solving
sx = 0

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

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

Simplifying
0 = -1sx

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 '(-2co + c2o2sx + -1i2n2sx)' equal to zero and attempt to solve:

Simplifying
-2co + c2o2sx + -1i2n2sx = 0

Solving
-2co + c2o2sx + -1i2n2sx = 0

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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