2 . sin(α+β)=-sin[5π/4+β)-(π/4-α)]

3.tan(α+2β)= 1

4.( 1) Right = tan (α+β) (1-tan α tan β) = tan α+tan β = left.

(2)- 1

(3)-√3

5.( 1)4

(2)- 1

(3)- 1

(4) 1

6.( 1)9/5

(2)24/25

(3) √(2√2/3)

(4) 17/25

7. 1/2

8. Prove it yourself. I can't read the steps when I write. What a mess.

9.( 1)t∈[π/2+2kπ，3π/2+2kπ]，k∈{ Z]& lt； br/>； (2) Maximum value: 2+√2, minimum value: 2-√ 2.

1 1. Minimum positive period: π

Maximize: draw your own images, I can't type.

12.( 1)- 1

(2){x|2kπ≤x≤2kπ+2π/3，k∈Z}

I hope you are satisfied. If the answer is not enough, please contact me and I will improve the answer.