Question

How do you simplify the expression `secthetatanthetacsctheta`?

Answer 1

`=sec^2theta`

Explanation:

`secthetatanthetacsctheta`
`=1/costheta times sintheta/costheta times 1/sintheta`
`=1/costheta times cancelsintheta/costheta times 1/cancelsintheta`
`=1/cos^2theta`
`=sec^2theta`

Answer 2

`sec^2(theta)`

Explanation:

`sec(theta)->1/cos(theta)`

`tan(theta)->(sin(theta))/(cos(theta))`

`csc(theta)->1/(sin(theta))`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Putting this all together gives:

`1/cos(theta)xx(cancel(sin(theta)))/cos(theta) xx1/(cancel(sin(theta))`

`=1/cos^2(theta) = sec^2(theta)`