Question

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

Answer 1

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

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