Question

Is it possible to verify:
(sin theta/1 + cos theta) +(1+cos theta/ sin theta)= 2csc theta.

Answer 1

Yes. Try your best to solve it and show me where you get stuck. Also, I suggest using more parentheses so that it's easier for me to read. So maybe like this:

[sin theta /(1+cos theta)] + ...

Answer 2

\[[(\sin \theta)/(1+\cos \theta)]* [(1-\cos \theta/\sin \theta)] +[(1+\cos \theta)/(\sin \theta)]*[(\sin \theta)/(1-\cos \theta)]\] ?

Answer 3

\[\Large\rm \frac{\sin \theta}{1+\cos \theta}+\frac{1+\cos \theta}{\sin \theta}\]Hmmmm not sure what you were trying to do there >.<
If you're going to multiply top and bottom by something, they need to be the same.
Example: (1-cosx)/(1-cosx).

Try to remember conjugates! You're usually trying to get back to your Pythagorean Identity whenever you see 1+cos or 1+sin

Answer 4

\[\Large\rm \frac{\sin \theta}{1+\cos \theta}\color{royalblue}{\left(\frac{1-\cos \theta}{1-\cos \theta}\right)}+\frac{1+\cos \theta}{\sin \theta}\]I would probably give the first fraction this, the conjugate of the bottom.
It should help clean things up.

Answer 5

Oh okay, sorry. Thank you for clearing that up for me! I'll try reworking it now.