If sin (2x) = cos (x + 30°), what is the value of x?

x = - 10 ° + π/6 + (2 π n_1) / 3 for n_1 element Z

or x = 30 ° + π/2 + 2 π n_2 for n_2 element Z

Step-by-step explanation:

Solve for x:

sin (2 x) = cos (x + 30 °)

Rewrite the right hand side using cos (θ) = sin (θ + π/2):

sin (2 x) = sin (30 ° + π/2 + x)

Take the inverse sine of both sides:

2 x = - 30 ° + π/2 - x + 2 π n_1 for n_1 element Z

or 2 x = 30 ° + π/2 + x + 2 π n_2 for n_2 element Z

Add x to both sides:

3 x = - 30 ° + π/2 + 2 π n_1 for n_1 element Z

or 2 x = 30 ° + π/2 + x + 2 π n_2 for n_2 element Z

Divide both sides by 3:

x = - 10 ° + π/6 + (2 π n_1) / 3 for n_1 element Z

or 2 x = 30 ° + π/2 + x + 2 π n_2 for n_2 element Z

Subtract x from both sides:

Answer: x = - 10 ° + π/6 + (2 π n_1) / 3 for n_1 element Z

or x = 30 ° + π/2 + 2 π n_2 for n_2 element Z