Respuesta :

sin(a + b) = sin(a)cos(b) + sin(b)cos(a)
sin(x + pi) = sin(x)cos(pi) + cos(x)sin(pi)

sin(pi) = 0cos(pi) = -1

sin(x + pi) = sin(x)(-1) + cos(x)(0)
sin(x + pi) = -sin(x) + 0
facundo3141592

By using the sine of the sum formula, we prove the given relation.

How to prove the trigonometric relation?

Here we need to use the formula.

sin(a + b) = sin(a)*cos(b) + sin(b)*cos(a)

If we apply that to the left side of the equation, we get:

sin(x + pi) = sin(x)*cos(pi) + sin(pi)*cos(x).

Now remember that:

  • cos(pi) = -1
  • sin(pi) = 0

Then:

sin(x + pi) = sin(x)*cos(pi) + sin(pi)*cos(x) = -sin(x)

sin(x + pi) = -sin(x).

So we just prove the above relation.

If you want to learn more about trigonometry, you can read:

https://brainly.com/question/13276558

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