Please help! I've been stuck for hours!
I need to prove the following identities and I've tried everything and can't get them to work!
(the * will stand for theta)

.) sin*+cos*cot*=csc*


.. ) 1/(1+cos*) + 1/(1-cos*)=2csc2*


... ) 1/(sin*) - 1/(tan*)=1


... ) sin*/(sin*-cos*)= 1/(1-cot*)


Please help!

I usually don't like doing homework on this site for people...

but I've had a pretty good day so far, so I'll help you out with the first one.

remember that cot = 1/tan = cos/sin
remember that csc = 1/sin

so

sin* + (cos*)(cos*/sin*) = 1/sin*

multiply the entire thing by sin*

sin^2* + cos^2* = sin*/sin*

sin^2 + cos^2 = 1

this is true.

these all are very simple
1. let take the left hand side
sin*+cos* cot*
sin* + cos* . Cos*/sin*
taking LCM
sin^* + cos^* / sin* as sin^*+cos^* = 1
1/sin*
cosec* proved


2. 1/(1+cos*) + 1/(1-cos*)=2csc^*



again take left hand side to prove
aftre take lcm it will be

(1-cos*) + (1+cos*)
------------------------
( 1-cos*) ( 1+cos*)

2
-------------
(1-cos^*)

2/sin^*

2cosec^* proved

3. 1/(sin*) - 1/(tan*)=1

seems incomplete question


4. sin*/(sin*-cos*)= 1/(1-cot*)

take rhs this time
1/(1-cot*)


1
--- as cot* = cos*/sin*
1- cos*/sin*


taking LCm & cross mltipcation

sin*/sin* -cos* proved