Voldemort

That is not a valid answer. You need to simplify it as much as you can. 

Sorry, I do not see a diagram, could you give the asymptote code or the image itself?

I agree with that answer as well. Both of the factors will always result in a result greater than or equal to 0. 

Ahh, an interesting question. Let's go through this step by step. What can you say about the numbers on the nth row of the pascal triangle?

Simplify the expressions and see what happens :D

sqrt(196)  is not 12! Try again!

Yep, another way you could solve it is by noting that:

tan(8pi/24) = ( tan(pi/24) + tan (7pi/24) )/ ( 1 - tan(pi/24)tan (7pi/24) )

Express the tan's in terms of sine and cosine, and use the sum to product identities :)

Before you start begging like some crazy dude, think about the problem. 

Express those terms in the form of sine and cosine, then try to express these terms using half angle identities. If you're unable to do this, you may need to try easier problems and work your way up from there. :)

There is definitely no relation to pascal's identity  in this problem. That identity would be used, when there is a sum rather than a product.

50 C 10 = (50 * 49 * 48 * 47 * 46 * 45 * 44 * 43 * 42 * 41)/(10!).

Multiplying 1/5 to 50 gives us:

(10 * 49 * 48 * 47 * 46 * 45 * 44 * 43 * 42 * 41)/(10 * 9 .... * 1). The 10 terms cancel out. 

(49 * 48 * 47 .... * 41)(9 * 8 *... * 1)  = 49 C 9.

That is correct, I don't know what's wrong?