Question

How do you simplify the expression `(tant+1)/sect`?

Answer 1

`sint+cost`

Explanation:

Starting with the beginning expression, we replace `tant` with `sint/cost` and `sect` with `1/cost`

`(tant+1)/sect` = `(sint/cost+1)/(1/cost)`

Getting a common denominator in the numerator and adding,
`color(white)(aaaaaaaa)`=`(sint/cost+cost/cost)/(1/cost)`

`color(white)(aaaaaaaa)`= `((sint+cost)/cost)/(1/cost)`
Dividing the numerator by the denominator,
`color(white)(aaaaaaaa)`=`(sint+cost)/cost-:(1/cost)`
Changing the divide to a multiply and inverting the fraction,
`color(white)(aaaaaaaa)`=`(sint+cost)/costxx(cost/1)`
We see the `cost` cancels out, leaving the resulting simplified expression.
`color(white)(aaaaaaaa)`=`(sint+cost)/cancel(cost)xx(cancel(cost)/1)`
`color(white)(aaaaaaaa)`=`(sint+cost)`