2sin(4x)sin(2x)-2cos(4x)cos(2x)=sqrt(2)

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Solution for 2sin(4x)sin(2x)-2cos(4x)cos(2x)=sqrt(2) equation:


Simplifying
2sin(4x) * sin(2x) + -2cos(4x) * cos(2x) = sqrt(2)

Remove parenthesis around (4x)
2ins * 4x * sin(2x) + -2cos(4x) * cos(2x) = sqrt(2)

Remove parenthesis around (2x)
2ins * 4x * ins * 2x + -2cos(4x) * cos(2x) = sqrt(2)

Reorder the terms for easier multiplication:
2 * 4 * 2ins * x * ins * x + -2cos(4x) * cos(2x) = sqrt(2)

Multiply 2 * 4
8 * 2ins * x * ins * x + -2cos(4x) * cos(2x) = sqrt(2)

Multiply 8 * 2
16ins * x * ins * x + -2cos(4x) * cos(2x) = sqrt(2)

Multiply ins * x
16insx * ins * x + -2cos(4x) * cos(2x) = sqrt(2)

Multiply insx * ins
16i2n2s2x * x + -2cos(4x) * cos(2x) = sqrt(2)

Multiply i2n2s2x * x
16i2n2s2x2 + -2cos(4x) * cos(2x) = sqrt(2)

Remove parenthesis around (4x)
16i2n2s2x2 + -2cos * 4x * cos(2x) = sqrt(2)

Remove parenthesis around (2x)
16i2n2s2x2 + -2cos * 4x * cos * 2x = sqrt(2)

Reorder the terms for easier multiplication:
16i2n2s2x2 + -2 * 4 * 2cos * x * cos * x = sqrt(2)

Multiply -2 * 4
16i2n2s2x2 + -8 * 2cos * x * cos * x = sqrt(2)

Multiply -8 * 2
16i2n2s2x2 + -16cos * x * cos * x = sqrt(2)

Multiply cos * x
16i2n2s2x2 + -16cosx * cos * x = sqrt(2)

Multiply cosx * cos
16i2n2s2x2 + -16c2o2s2x * x = sqrt(2)

Multiply c2o2s2x * x
16i2n2s2x2 + -16c2o2s2x2 = sqrt(2)

Reorder the terms:
-16c2o2s2x2 + 16i2n2s2x2 = sqrt(2)

Reorder the terms for easier multiplication:
-16c2o2s2x2 + 16i2n2s2x2 = 2qrst

Solving
-16c2o2s2x2 + 16i2n2s2x2 = 2qrst

Solving for variable 'c'.

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

Add '-16i2n2s2x2' to each side of the equation.
-16c2o2s2x2 + 16i2n2s2x2 + -16i2n2s2x2 = -16i2n2s2x2 + 2qrst

Combine like terms: 16i2n2s2x2 + -16i2n2s2x2 = 0
-16c2o2s2x2 + 0 = -16i2n2s2x2 + 2qrst
-16c2o2s2x2 = -16i2n2s2x2 + 2qrst

Divide each side by '-16o2s2x2'.
c2 = i2n2o-2 + -0.125o-2qrs-1tx-2

Simplifying
c2 = i2n2o-2 + -0.125o-2qrs-1tx-2

Reorder the terms:
c2 + -1i2n2o-2 + 0.125o-2qrs-1tx-2 = i2n2o-2 + -1i2n2o-2 + -0.125o-2qrs-1tx-2 + 0.125o-2qrs-1tx-2

Combine like terms: i2n2o-2 + -1i2n2o-2 = 0
c2 + -1i2n2o-2 + 0.125o-2qrs-1tx-2 = 0 + -0.125o-2qrs-1tx-2 + 0.125o-2qrs-1tx-2
c2 + -1i2n2o-2 + 0.125o-2qrs-1tx-2 = -0.125o-2qrs-1tx-2 + 0.125o-2qrs-1tx-2

Combine like terms: -0.125o-2qrs-1tx-2 + 0.125o-2qrs-1tx-2 = 0.000
c2 + -1i2n2o-2 + 0.125o-2qrs-1tx-2 = 0.000

The solution to this equation could not be determined.

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