Question

simplify \\( \sin ( u - \pi ) \\) to a single trig function using a sum or difference of angles identity.

Explanation:

Step1: Use the sine difference identity

The sine difference identity is $\sin(A - B)=\sin A\cos B-\cos A\sin B$. Here $A = u$ and $B=\pi$. So, $\sin(u-\pi)=\sin u\cos\pi-\cos u\sin\pi$.

Step2: Substitute the values of $\cos\pi$ and $\sin\pi$

We know that $\cos\pi=- 1$ and $\sin\pi = 0$. Substituting these values into the expression from Step1: $\sin u\times(-1)-\cos u\times0$.

Step3: Simplify the expression

$\sin u\times(-1)-\cos u\times0=-\sin u - 0$.

Answer:

$-\sin u$