Question

I need help understanding how to convert the expressions so they can cancel out in order to achieve the answer

Answer 1

Recall the equivalent expression of each term.

$cos\beta=\frac{x}{r}$$tan\beta=\frac{y}{x}$$csc\beta=\frac{r}{y}$$cot\beta=\frac{x}{y}$

Using their equivalents, we can rewrite the expression as:

$(\frac{x}{r})(\frac{y}{x})(\frac{r}{y})(\frac{x}{y})$

Then, multiply the variables.

$\frac{x^2yr}{xy^2r}$

Then, simplify by subtracting the exponents of each respective variable. The result is:

$\frac{x}{y}$

Since x/y is equivalent to cot β, then the given trigonometric expression is just equal to cot (β).