Question

Question #13e99

Answer 1

see explanation...

Explanation:

First, multiply out in the numerator:

`(sin(t) + cos(t))^2/(sin(t)cos(t)) = (sin^2(t) + 2sin(t)cos(t) + cos^2(t))/(sin(t)cos(t) )`

Re-order the terms in the numerator a bit, and use the fact that `sin^2(t) + cos^2(t) = 1`, giving:

`(1 + 2sin(t)cos(t))/(sin(t)cos(t))`
`=1/((sin(t)cos(t)) )+ (2(sin(t)cos(t)))/(sin(t)cos(t))`

...you can now factor/separate the first term. Also, note that in the right term, the `sin(t)cos(t)` in numerator and denominator cancels out. So you have:

`(1/sin(t)) * (1/cos(t)) + 2`

...now remember `1/cos(t) = sec(t)`, and `1/sin(t) = csc(t)`, so it all works out to:

`csc(t)sec(t) + 2`

GOOD LUCK