Pre-calculus identities help?

Question

I have a take home test I'm trying to do and I have most of it done but I need some help with these.

These are establishing identities

0=theta

1. Cos0(1 + tan^2 0) = 1

2. (sin0)/(1+cos0) + (1 + cos0)/(sin0) = 2csc0

These are sum and difference I think. There are a few of these but I hopefully I can figure the rest out.
a= alpha B = beta

Find sin (a + B), cos (a + B), sin (2a), cos(2a), sin (B/2)

3. Tan(a) = -2 Pi/2 < a < pi
CotB = -2. Pi/2 < B < pi

Answer 1

3.

Tan(a) = -2    π/2 < a < π   -(1)

CotB = -2      π/2 < B < π   -(2)

Recall : Trigonometry identities sec^2a = 1 + tan²a

Sec²(a) = 1 + (-2)²

                 = 1 + 4

                = 5

seca = √5

cosa = ±(1 / √5)

sina = √( 1 - cos²a)

        = √(1 - (1 / 5)

        = √4 / 5

       = ±(2 / √5)

cos(2a) = cos²a - sin²a

              = 1 / 5 - 4 / 5

              = -3 / 5.

Answer 2

3.

Tan(a) = -2    π/2 < a < π   -(1)

CotB = -2      π/2 < B < π   -(2)

Recall : Trigonometry identities csc^2B = 1 + Cot²B

Csc²(B) = 1 + (-2)²

                 = 1 + 4

                = 5

CscB = ±√5

sinB = ±(1 / √5)

cosB= √( 1 - sin²B)

        = √(1 - (1 / 5)

        = √4 / 5

       = ±(2 / √5)

Sin(B / 2) = √(1 - cosB) / 2

                = √[(1 - 2 / √5) / 2] or √[(1 + 2 / √5) / 2 ].