Question

Prove that cosecant^2 x divided by cotangent x = cosecant x times secant x

Answer 1

`\bf \cfrac{csc^2(x)}{cot(x)}=csc(x)sec(x)\\\\ -----------------------------\\\\ cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)} \qquad \qquad % cosecant csc(\theta)=\cfrac{1}{sin(\theta)}\\\\ -----------------------------\\\\ thus \\\\\\ \cfrac{(1^2)/(sin^2(x))}{(cos(x))/(sin(x))}\implies \cfrac{1}{sin^2(x)}\cdot \cfrac{sin(x)}{cos(x)}\implies \cfrac{1}{sin(x)cos(x)} \\\\\\ \cfrac{1}{sin(x)}\cdot \cfrac{1}{cos(x)}`

and surely, you know what that is