Thread: Need help getting started identities.

1. Need help getting started identities.

Hey guys,
I need some help getting started with proving this identity problem. Everytime I get started I feel like I am just making it uglier
((1 +sin theta)/(1-sin theta))-((1-sin theta)/(1+sin theta)=4*tan theta*sec theta

Thanks for your help!

~Nikki

2. Re: Need help getting started identities.

I'll write x instead of theta
Put the left hand side onto a common denominator of (1-sinx)(1+sinx) and simplify your numerator.
Note this common denominator will also simplify to 1-sin^2x which= cos^2x

3. Re: Need help getting started identities.

Starting with the LHS get a common denominator, namely $(1-\sin\theta)(1+\sin\theta)$.

Expand and simplify the numerator and you should be done.

Post again if you're still stuck.

4. Re: Need help getting started identities.

Thank you very much! I think I got it, I ended up with -(4sinx)/(cosx)^2=4tanx*secx

5. Re: Need help getting started identities.

So I would do the same thing for this problem right? find the common denominator on the LHS? ((sinx+cosx)/sinx) - ((cosx-sinx)/cosx)=secx*cscx