Sin (18m-12) cos (7m+2) find the value of m

m = - 2/7 + π/14 + (π n_1) / 7 for n_1 element Z

or m = 2/3 - (π n_2) / 18 for n_2 element Z

Step-by-step explanation:

Solve for m:

-cos (7 m + 2) sin (12 - 18 m) = 0

Multiply both sides by - 1:

cos (7 m + 2) sin (12 - 18 m) = 0

Split into two equations:

cos (7 m + 2) = 0 or sin (12 - 18 m) = 0

Take the inverse cosine of both sides:

7 m + 2 = π n_1 + π/2 for n_1 element Z

or sin (12 - 18 m) = 0

Subtract 2 from both sides:

7 m = - 2 + π/2 + π n_1 for n_1 element Z

or sin (12 - 18 m) = 0

Divide both sides by 7:

m = - 2/7 + π/14 + (π n_1) / 7 for n_1 element Z

or sin (12 - 18 m) = 0

Take the inverse sine of both sides:

m = - 2/7 + π/14 + (π n_1) / 7 for n_1 element Z

or 12 - 18 m = π n_2 for n_2 element Z

Subtract 12 from both sides:

m = - 2/7 + π/14 + (π n_1) / 7 for n_1 element Z

or - 18 m = π n_2 - 12 for n_2 element Z

Divide both sides by - 18:

Answer: m = - 2/7 + π/14 + (π n_1) / 7 for n_1 element Z

or m = 2/3 - (π n_2) / 18 for n_2 element Z