Calc 1 Trig Substitution

[VivaTequila]

Asked to simplify: Cos^2(x)/sin(x) + sin(x)
Answer is cosec^2(x)

I understand that if you divide both terms by sin(x), you get:
cot(x)+1

which is equivalent to cosec^2(x)

but why is it that when you multiply both terms by sin(x), you get cos^2(x)+sin^2(x), which is 1, which is not cosec^2(x) - the answer...

cheers

[b^3]

Are you sure is the answer?
Wouldn't it just be ?

I understand that if you divide both terms by sin(x), you get:
cot(x)+1

which is equivalent to cosec^2(x)

Also note that when you divide by sin(x), that , it's


Also just to make sure I'm not seeing things, http://www.wolframalpha.com/input/?i=cos%5E2(x)%2Fsin(x)%2Bsin(x)&t=crmtb01

So the answer is not

[VivaTequila]

right you are, thanks for the speedy reply!

and hmm...

why is it that the sin(x) doesn't cancel out?