Amagician showed a magic trick where he picked one card from a standard deck. determine what the probablity is that the catd will be a black queen card?

Just tell me how to set up the equation.

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

Prove sin2a + cos2a - 1 / sin2a + cos2a + 1 = 1 - tana / 1 + cota