Answer: [tex]-4\sin \left(\frac{a}{2}\right)\sin \left(\frac{\pi -a}{2}\right)\cos \left(a\right)[/tex]
Step-by-step explanation:
We need to use trig identities (converting sin to cosine) in order to simplify this expression.
Solving:
Given : [tex]\(4 \sin\left(\frac{a}{2}\right) \sin\left(\frac{\pi - a}{2}\right) \sin\left(\frac{3\pi}{2} - a\right)\)[/tex]
First, let's rewrite the expression:
[tex]\[ 4 \sin\left(\frac{a}{2}\right) \sin\left(\frac{\pi - a}{2}\right) \sin\left(\frac{3\pi}{2} - a\right) \][/tex]
Now, we can use the identity: [tex]\(\sin(\pi - x) = \sin(x)\) and \(\sin(3\pi/2 - a) = \text-cos(a)\)[/tex]
[tex]\[ 4 \sin\left(\frac{a}{2}\right) \sin\left(\frac{\pi - a}{2}\right) \((-cos(a)) \][/tex]
This is equivalent to the expression: [tex]\( -4\sin \left(\frac{a}{2}\right)\sin \left(\frac{\pi -a}{2}\right)\cos \left(a\right)\)[/tex]
That's it!
