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

Answer 1

To show that sin(x + π) = -sin(x), we need to use the sum-to-product trigonometric identity and the periodicity of sine function.

According to the sum-to-product trigonometric identity, sin(A + B) = sinA cosB + cosA sinB.

Therefore, we can write sin(x + π) as sinx cosπ + cosx sinπ.

Since cos(π) = -1 and sin(π) = 0, the expression becomes sinx (-1) + cosx (0), which simplifies to -sinx.

Thus, sin(x + π) = -sinx.