Question

Question #88b3e

Answer 1

`1/cosx`

Explanation:

Convert everything to `sinx` and `cosx`:

`(sinx/cosx+cosx/sinx)/(1/sinx)`

Dividing by `1/sinx` is the same as multiplying by the reciprocal `sinx`

`(sinx)(sinx/cosx+cosx/sinx)`

Distribute

`sin^2x/cosx+(sinxcosx)/sinx`

Simplify

`sin^2x/cosx+cosx/1`

The common denominator is `cosx`

`sin^2x/cosx+cos^2x/cosx`

Add fractions

`(sin^2x+cos^2x)/cosx`

`sin^2x+cos^2x=1` (Pythagorean Identity) Sooooo:

`(sin^2x+cos^2x)/cosx=1/cosx`

That's your answer in terms of `cosx`. Most people would convert `1/cosx` to `secx`, though.