Answer:
Steps shown below
Step-by-step explanation:
We will simplify this using definitions and identities. Let's start.
[tex]\frac{cos(x)}{sin(x)tan(x)}[/tex]
Using [tex]tanx=\frac{sinx}{cosx}[/tex], we have:
[tex]\frac{cos(x)}{sin(x)\frac{sin(x)}{cos(x)}}\\=\frac{cos^2(x)}{sin^2(x)}[/tex]
Using [tex]cot(x)=\frac{cos(x)}{sin(x)}[/tex], we have:
[tex]\frac{cos^2(x)}{sin^2(x)}\\=cot^2(x)[/tex]
Hence, proved.
