cosx*cosx*3-sinx*sinx*3=0

Solution for cosx*cosx*3-sinx*sinx*3=0 equation:

Simplifying
cosx * cosx * 3 + -1sinx * sinx * 3 = 0

Reorder the terms for easier multiplication:
3cosx * cosx + -1sinx * sinx * 3 = 0

Multiply cosx * cosx
3c2o2s2x2 + -1sinx * sinx * 3 = 0

Reorder the terms for easier multiplication:
3c2o2s2x2 + -1 * 3insx * insx = 0

Multiply -1 * 3
3c2o2s2x2 + -3insx * insx = 0

Multiply insx * insx
3c2o2s2x2 + -3i2n2s2x2 = 0

Solving
3c2o2s2x2 + -3i2n2s2x2 = 0

Solving for variable 'c'.

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

Add '3i2n2s2x2' to each side of the equation.
3c2o2s2x2 + -3i2n2s2x2 + 3i2n2s2x2 = 0 + 3i2n2s2x2

Combine like terms: -3i2n2s2x2 + 3i2n2s2x2 = 0
3c2o2s2x2 + 0 = 0 + 3i2n2s2x2
3c2o2s2x2 = 0 + 3i2n2s2x2
Remove the zero:
3c2o2s2x2 = 3i2n2s2x2

Divide each side by '3o2s2x2'.
c2 = i2n2o-2

Simplifying
c2 = i2n2o-2

Take the square root of each side:
c = {-1ino-1, ino-1}