Question

Help this is my homework I been struggling and I can not find the mistake I will appreciate it!

Answer 1

The formula for the sum of angles in cosine is:

$\cos (a+b)=\cos (a)\cdot\cos (b)-\sin (a)\cdot\sin (b)$

So in this case the error is adding instead of substracting.

Let's correct it:

$\cos (x+\frac{3\pi}{2})=\cos (x)\cos (\frac{3\pi}{2})-\sin (x)\sin (\frac{3\pi}{2})$

$\cos (x+\frac{3\pi}{2})=\cos (x)\cdot0-\sin (x)\cdot-1$

$\cos (x+\frac{3\pi}{2})=\sin (x)$