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:

 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

answer: that was hard but still working on it

step-by-step explanation:

(a) the volume of the cone is 20/3 in3

hence, option a is correct.