Question

How do you simplify the expression `secthetacottheta`?

Answer 1

`csctheta`

Explanation:

Using the `color(blue)"trigonometric identities"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(sectheta=1/(costheta)" and " cottheta=(costheta)/(sintheta))color(white)(a/a)|)))`

`rArrsecthetacottheta=1/(cancel(costheta))xxcancel(costheta)/sintheta=1/(sintheta)`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(csctheta=1/(sintheta))color(white)(a/a)|)))`

`rArr1/(sintheta)=csctheta`

Thus: `secthetacottheta=csctheta`