Question

Tried a lot of different ways to solve the problem but the portal kept saying my answer was wrong, I need an answer with steps.

Answer 1

Answer: $-4\sin \left(\frac{a}{2}\right)\sin \left(\frac{\pi -a}{2}\right)\cos \left(a\right)$

Step-by-step explanation:

We need to use trig identities (converting sin to cosine) in order to simplify this expression.

Solving:

Given : $\(4 \sin\left(\frac{a}{2}\right) \sin\left(\frac{\pi - a}{2}\right) \sin\left(\frac{3\pi}{2} - a\right)\)$

First, let's rewrite the expression:

$\[ 4 \sin\left(\frac{a}{2}\right) \sin\left(\frac{\pi - a}{2}\right) \sin\left(\frac{3\pi}{2} - a\right) \]$

Now, we can use the identity: $\(\sin(\pi - x) = \sin(x)\) and \(\sin(3\pi/2 - a) = \text-cos(a)\)$

$\[ 4 \sin\left(\frac{a}{2}\right) \sin\left(\frac{\pi - a}{2}\right) \((-cos(a)) \]$

This is equivalent to the expression: $\( -4\sin \left(\frac{a}{2}\right)\sin \left(\frac{\pi -a}{2}\right)\cos \left(a\right)\)$

That's it!