Question

If italic sin open parentheses 2 x close parentheses equal italic cos open parentheses x plus 30 degree close parentheses comma what is the value of x?.

Answer 1

Using complementary angles, it is found that the solution to the trigonometric equation is of x = 20.

What are complementary angles?

Complementary angles are two angles whose measures add to 90º.

If two angles a and b are complementary, we have that the sine of one is the cosine of other, that is:

$\sin{a} = \cos{b}$

In this problem, the equation is:

$\sin{(2x)} = \cos{(x + 30)}$

Hence, they are complementary, which means that:

$2x + x + 30 = 90$

$3x = 60$

$x = \frac{60}{3}$

$x = 20$

The solution to the trigonometric equation is of x = 20.

More can be learned about complementary angles at brainly.com/question/11161460