Question

How do you prove `sin theta sec theta- tan theta`?

Answer 1

Assuming the minus sign should be an equal sign, so the question is to prove:
`color(white)("XXXX")` `sin(theta)sec(theta) = tan(theta)`

`sec(theta) = 1/cos(theta)` `color(white)("XXXX")`(basic definition)

`sin(theta) * sec(theta)`
`color(white)("XXXX")` `= sin(theta) * 1/cos(theta)`

`color(white)("XXXX")` `= sin(theta)/cos(theta)`

`color(white)("XXXX")` `= tan(theta)`