Question

How do you simplify the expression `(sec^3x-secx)/(5secx)`?

Answer 1

Please the explanation for the process

Answer: `1/5tan^2(x)`

Explanation:

Remove a common factor of `sec(x)` from the numerator, because we know that `sec(x)/sec(x) = 1`:

`(sec(x)(sec^2(x) - 1))/(5sec(x)) = 1/5(sec^2(x) - 1)`

Substitute `tan^2(x)` for `(sec^2(x) - 1)`:

`1/5tan^2(x)`