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
