Question

Simplify the expression please.

Answer 1

tanx·secx

Explanation:

To simply this, you can begin by factoring sin x out of the numerator to become:

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

Now, using Pythagorean Trig Identities, we know that sin²x+cos²x equals 1. We can substitute this to make the equation become:

`(sinx)/(cos^(2)x )`

First of all, we can convert
`(sinx)/(cosx)` to tanx. However, we have a remaining
`(1)/(cosx)` which, using reciprocal identities, will become sec x.

Finally, we get our answer as tanx·secx.