Question

Help! If you know this can you tell me how to do it?

Answer 1

c

Explanation:

Here's how this works:

Get everything together into one fraction by finding the LCD and doing the math. The LCD is sin(x) cos(x). Multiplying that in to each term looks like this:

`[sin(x)cos(x)](sin(x))/(cos(x))+[sin(x)cos(x)](cos(x))/(sin(x)) =?`

In the first term, the cos(x)'s cancel out, and in the second term the sin(x)'s cancel out, leaving:

`(sin^2(x))/(sin(x)cos(x))+(cos^2(x))/(sin(x)cos(x))=?`

Put everything over the common denominator now:

`(sin^2(x)+cos^2(x))/(sin(x)cos(x))=?`

Since
`sin^2(x)+cos^2(x)=1`, we will make that substitution:

`(1)/(sin(x)cos(x))`

We could separate that fraction into 2:

`(1)/(sin(x))`×
`(1)/(cos(x))`

`(1)/(sin(x))=csc(x)` and
`(1)/(cos(x))=sec(x)`

Therefore, the simplification is

sec(x)csc(x)