Answer
$\sin (s+t)=\sin s \sin t+\cos s \cos t$
Work Step by Step
Use the identity $\cos (x+h)=\cos x \cos h+\sin x \sin h$
As we are given that $\sin x=\cos (\dfrac{\pi}{2}-x)$
and $\cos x=\sin (\dfrac{\pi}{2}-x)$
Now, $\sin (s+t)=\cos (\dfrac{\pi}{2}-(s+t))$
Consider
$\cos [(\dfrac{\pi}{2}-s)+t)]=\cos (\dfrac{\pi}{2}-s) \cos t+\sin (\dfrac{\pi}{2}-s) \sin t$
Thus,
Hence, $\sin (s+t)=\sin s \sin t+\cos s \cos t$
