advanced functions Trigonometry proving question.

[jsamplonius]

I was given this question in a review and couldn't get the answer. it would be greatly appreciated if you could show all the work and the answer. please and thankyou.

1 + (cotx)(tany) = sin (x+y)
sinx cosy

my teacher advised using the left side, right side technique to get the answer but this is all i had.
Left Side
1 + cotx tany

1 + cosx x siny
sinx cosy

1 + cosx siny sinx cosy

 

[ksdhart]

I'm not 100% sure what the problem you're trying to prove is... I'm assuming it's this. If not, please clarify so we're working the same problem.

\(\displaystyle 1+cot\:x\:tan\:y=\frac{sin\left(x+y\right)}{sin\:x\:cos\:y}\)

If this is your problem, then the work you did on the left side looks good. You say you're stuck and don't know how to transform it any further... so, what if you work the right side instead? Use the sum formula for angles to get:

\(\displaystyle \frac{sin\left(x+y\right)}{sin\:x\:cos\:y}=\frac{sin\:x\:cos\:y\:+\:cos\:x\:sin\:y}{sin\:x\:cos\:y}\)

Try working it from there. You're really close to the answer.

 

[vomv1988]

Trigonometric identity proof

I was given this question in a review and couldn't get the answer. it would be greatly appreciated if you could show all the work and the answer. please and thankyou.

1 + (cotx)(tany) = sin (x+y)
sinx cosy

my teacher advised using the left side, right side technique to get the answer but this is all i had.
Left Side
1 + cotx tany

1 + cosx x siny
sinx cosy

1 + cosx siny sinx cosy

Your typesetting is pretty unclear. But I'll assume you meant something like:



If that's the case, then you'll want to use the following trigonometric identities (from wikipedia):

1.

2.

3.

The proof goes something like:

From 3:







From 1 and 2:





Try using something like this next time to typeset your math.

 

[jsamplonius]

this is my question, but i still cant get any farther. im not sure what to do as if i do what you laid out i get cosxsiny. does the left side need to go farther yet?

 

[jsamplonius]

I found my mistake and came to the answer after. thanks for your help