Rewrite csc theta/cot theta in terms of sine and cosine

Cot (theta) - csc (theta) = cos(theta) divided by sin(theta) - 1 divided by sin(theta) = cos(theta) - 1 divided by sin(theta) = the square root of 1-sin^2 (theta) -1 divided by sin(theta)

The table shows the results of (p ^ q) and results of  (p ^ r) for all possible outcomes. We have to tell which of the outcomes of union of both these events will always be true.

(p ^ q) V (p ^ r) means Union of (p ^ q) and (p ^ r). The property of Union of two sets/events is that it will be true if either one of the event or both the events are true i.e. there must be atleast one True(T) to make the Union of two sets to be True. 

So, (p ^ q) V (p ^ r)  will be TRUE, if either one of  (p ^ q) and (p ^ r)  or both are true. From the given table we can see that only the outcomes A, B and C will result is TRUE. The rest of the outcomes will all result in FALSE.

Therefore, the answer to this question is option 2nd