Is there a simple way to understand the trigonometric identities?
Yes, all can be made out of the Pythagoras Theorem.
Does the time taken for emptying a vessel depend upon the shape of the vessel, given that it has the same volume of water in it?
Yes. A differential equation is to be formulated which would treat the rate of change of volume as a variable and the decrease in height as a function of time. Both of them have to be solved together to find the time taken for each container to get empty.
Can two light waves meet and still create darkness?
Yes. That's what is called as the interference of light.