Need some help on proving these, I know pythagorean identities, but I'm lost on these, I know that cos(x) = cos(-x) (Headbang)

1) If cos( alpha + beta) = cos (alpha) cos (beta) - sin(alpha) sin (beta), show that cos (2t) = cos^2 (t) - sin^2 (t)

2) If sin (alpha + beta) = sin (alpha) cos(beta) + cos (alpha) sin (beta), show that sin (2t) = 2 sin (t) cos (t)

and also if anyone can help on these that would be great too

3. Find all values that sin (alpha) = sin (2 alpha)

4. Find all values that cos (2 alpha) = cos (alpha)

5. Show cos^2 (t) = [1 + cos (2t)]/2

6. Show sin^2 (t) = [1 - cos (2t)]/2