Using complementary angles, it is found that the solution to the trigonometric equation is of x = 20.
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:
[tex]\sin{a} = \cos{b}[/tex]
In this problem, the equation is:
[tex]\sin{(2x)} = \cos{(x + 30)}[/tex]
Hence, they are complementary, which means that:
[tex]2x + x + 30 = 90[/tex]
[tex]3x = 60[/tex]
[tex]x = \frac{60}{3}[/tex]
[tex]x = 20[/tex]
The solution to the trigonometric equation is of x = 20.
More can be learned about complementary angles at https://brainly.com/question/11161460
