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Which of the following could be solution to the equation below?
[tex]cos(3x+4)=sin(2x+6)[/tex]

A. x = 2, sin 10° = cos 10°
B. x = 16, sin 52° = cos 38°
C. x = 34, sin 74° = cos 106°
D. x = 16, sin 38° = cos 52°

Respuesta :

Using complementary angles, it is found that a solution to the given equation is:

D. x = 16, sin 38° = cos 52°.

What are complementary angles?


Two angles are called complementary if the sum of their measures is of 90º. If two angles A and B are complementary, we have that:

cos(A) = sin(B) and sin(A) = cos(B).

In this problem, the expression is:

cos(3x + 4) = sin(2x + 6).

Hence:

3x + 4 + 2x + 6 = 90

5x = 80

x = 16.

Then:

  • cos(3x + 4) = cos(52).
  • sin(2x + 6) = sin(38).

Which means that option D is correct.

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

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