Question

cot 3pi/2-sin3pi/2

Answer 1

\(\sf cot = \frac{cos(x)}{sin(x)}\)

Answer 2

$$
\large{
\cos(a)-\sin(a)=-\sqrt(2)\sin(a-\cfrac{\pi}{4})
}
$$
Where \(a=\cfrac{3\pi}{2}\).

This comes from
$$
\sin(a-b)=\sin(a)\cos(b)-\sin(b)\cos(a)
$$
Does this help?