Ah, I've always sucked at doing proofs, so I'd like help with these two;

Prove that $\displaystyle sin^2 x (1 + cot^2x) = 1$

Prove that $\displaystyle tan x (cot x + tan x) = sec^2x$

Sorry that I haven't shown my beginning steps, I'll work on it while I wait for a response. Thanks in advance for any help