1) Write (cscX/cotX)-(cotX/cscX) in terms of sinX and cosX and simplify. I've tried it a few ways on this one but it never seems to get in any simpler form, I feel like I'm missing something.
I went through these steps:
(cscX/cotX)-(cotX/cscX)=(1/sinX)/(cosX/sinX)-(cosX/sinX)/(1/sinX)=(1/sinX)^2/(cosX/sinX)*(1/sinX)=((1/sinX)^2-(cosX/sinX)^2)/((cosX/sinX)*(1/sinX)) which simplfies to (1/sinX)-(cosX/sinX) which simplifies to 1-cosX right? Is that as far as I can go or is there an identity I'm missing for it? (actually, now that I think about it, is it possible to eliminate the denominator (cosX/sinX)*(1/sinX) because it is being multiplied?
2) Verify the identitiy (sinX/1-cosX)=(1+cosX/sinX). I'm just not sure where to go here either.
I went through these steps:
(cscX/cotX)-(cotX/cscX)=(1/sinX)/(cosX/sinX)-(cosX/sinX)/(1/sinX)=(1/sinX)^2/(cosX/sinX)*(1/sinX)=((1/sinX)^2-(cosX/sinX)^2)/((cosX/sinX)*(1/sinX)) which simplfies to (1/sinX)-(cosX/sinX) which simplifies to 1-cosX right? Is that as far as I can go or is there an identity I'm missing for it? (actually, now that I think about it, is it possible to eliminate the denominator (cosX/sinX)*(1/sinX) because it is being multiplied?
2) Verify the identitiy (sinX/1-cosX)=(1+cosX/sinX). I'm just not sure where to go here either.