prove the identity: sinxcosx + cos²x = cosx(1+cotx)/cscx

[trighelpp]

prove the identity: sinxcosx + cos²x = cosx(1+cotx)/cscx

Alright, here's the problem:
sinxcosx + cos²x = cosx(1+cotx)/cscx

Ok, I can change some of this to end up w/the structure and same terms needed at the end, but I don't know how to end up exactly right. I only end up with-
cosx + 1+cotx[all over]/cscx

how do I get the cosx and 1+cotx to be a product of each other rather than a sum? Am I missing something obvious, or do I need to switch some things up and start out differently? It seems easy and like it can be done in just a couple or few steps, but idk if it's easier than I'm making it out to be and I'm missing something or if it's more than what I'm making it to be?

 

[Deleted member 4993]

Re: Woah, ok now, one more trig identity and I'm straight

Alright, here's the problem:
sinxcosx + cos²x = cosx(1+cotx)/cscx

Ok, I can change some of this to end up w/the structure and same terms needed at the end, but I don't know how to end up exactly right. I only end up with-
cosx + 1+cotx[all over]/cscx <<< How did you get there - please show your work

 

[trighelpp]

Re: Woah, ok now, one more trig identity and I'm straight

Okay, here's what I did.
I started with the left side.
I changed sinx to 1/cscx, and I changed cos²x to 1+cotx.
So, I end up with cosx + 1+cotx[all over]/cscx.

But, I don't know how to change the cosx PLUS 1+cotx to being cosx TIMES 1+cotx.

 

[Deleted member 4993]

Re: Woah, ok now, one more trig identity and I'm straight

Okay, here's what I did.
I started with the left side.
I changed sinx to 1/cscx, and I changed cos²x to 1+cotx. <<< That is not a correct relationship

probably you are thinking about

csc[sup:3jlwa4zo]2[/sup:3jlwa4zo](x) = 1 + cot[sup:3jlwa4zo]2[/sup:3jlwa4zo](x)

But that is not applicable here - because you have cos[sup:3jlwa4zo]2[/sup:3jlwa4zo](x) NOT csc[sup:3jlwa4zo]2[/sup:3jlwa4zo](x)

So, I end up with cosx + 1+cotx[all over]/cscx.

This is NOT how you do mathematics - show me what you are doing without using words.

So If I get your steps - I see:

cos(x) * sin(x) + cos[sup:3jlwa4zo]2[/sup:3jlwa4zo](x)

= cos(x)/csc(x) + cos[sup:3jlwa4zo]2[/sup:3jlwa4zo](x)

Now what.....

But, I don't know how to change the cosx PLUS 1+cotx to being cosx TIMES 1+cotx.