I've always had problems with these. Surely it cant be that hard, but I really cant get my head around them as it stands, even if it is just proving them - Maybe because I cant find many practical uses for it.. Anyway, these are the following coursework questions due for tomorrow. Would be very greatful if you could provide full answers so I can actually start to understand these damned things. Cheers!

[Y=Theta]

12) Using double angle formulae rewrite $\displaystyle sin 4Y$ in terms of $\displaystyle sin Y$ and $\displaystyle cos Y$ (Raised to any power).

13) Prove the following identitys:

a) $\displaystyle cot^2 x+1 = cosec^2 x$

b) $\displaystyle (tan x+sec x)/(sec x-cos x+tan x) = cosec x$

c) $\displaystyle sin^3 x-cos^3 x = (1+sin x*cos x)(sin x-cos x)$

For c) we were told to go about doing the right hand side first.

Thanks again!