Question

(1/1+sinx)+tanx

Answer 1

Change everything in terms of sine and cosine.
So what is tanx in terms of sine/cosine?

Answer 2

sinx/cosx

Answer 3

Good, now we have this:
\[\frac{1}{1+sinx}+\frac{sinx}{cosx}\]

Answer 4

Now get common denominators

Answer 5

my bad the first term should be cosx in the numerator
and the common denom is just (1+sinx)(cosx)

Answer 6

So it's:
\[\frac{cosx}{1+sinx}+\frac{sinx}{cosx}\]?

Answer 7

yea

Answer 8

Alright, and yes you are correct the common denominator is (1+sinx)(cosx), now show me what you get as a result.

Answer 9

i get cosx^2+1+sinx^2 on top which equals 1+1 or maybe just 1 idk cus i feel the answer will end up being csc. and the denom i dont now what to do with cosx+sinxcosx

Answer 10

actually the top ends up cosx^2+sinx+sinx^2 which is just sinx

Answer 11

Well let's work it out:
So you were right the top does become cos^2x+sin^2x+sinx
\[\frac{\cos^2x+sinx+\sin^2x}{(1+sinx)(cosx)}\]
And be careful, it's not just sinx, do you remember what this equals?
\[\sin^2x+\cos^2x=?\]

Answer 12

o yea i forgot to leave the 1 when i used the identity

Answer 13

so the its just 1 over cosx which is secx

Answer 14

Correct so we get this:
\[\frac{1+sinx}{(1+sinx)(cosx)}\]

Answer 15

And yes, nice job :)

Answer 16

thanks man

Answer 17

Anytime :P