Solve sin (2x) cos (6x) - cos (2x) sin (6x) = -0.7

x = π/4 - 1/4 sin^ (-1) (7/10) + (π n_1) / 2 for n_1 element Z

or x = (π n_2) / 2 + 1/4 sin^ (-1) (7/10) for n_2 element Z

Step-by-step explanation:

Solve for x:

cos (6 x) sin (2 x) - cos (2 x) sin (6 x) = - 0.7

-0.7 = - 7/10:

cos (6 x) sin (2 x) - cos (2 x) sin (6 x) = - 7/10

Reduce trigonometric functions:

-sin (4 x) = - 7/10

Multiply both sides by - 1:

sin (4 x) = 7/10

Take the inverse sine of both sides:

4 x = π - sin^ (-1) (7/10) + 2 π n_1 for n_1 element Z

or 4 x = 2 π n_2 + sin^ (-1) (7/10) for n_2 element Z

Divide both sides by 4:

x = π/4 - 1/4 sin^ (-1) (7/10) + (π n_1) / 2 for n_1 element Z

or 4 x = 2 π n_2 + sin^ (-1) (7/10) for n_2 element Z

Divide both sides by 4:

Answer: x = π/4 - 1/4 sin^ (-1) (7/10) + (π n_1) / 2 for n_1 element Z

or x = (π n_2) / 2 + 1/4 sin^ (-1) (7/10) for n_2 element Z