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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?.

Sagot :

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:

[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

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