1 . cos(a-β)= cosa cosβ+Sina sinβ=(3/5)×(5/ 13)+(-4/5)×( 12/ 13)=-33/65

2. The original formula = cos [(61+2a)-(31+2a)] = cos 30 = √ 3/2.

3.∫cos(a-π/3)= cosa cos(π/3)+Sina sin(π/3)=( 1/2)cosa+(√3/2)Sina = cosa

∴(√3/2)sina=( 1/2)cosa

Tana =√3/3

4.sina= √ 1 - cos？ a= 3/5

∫a is an acute angle

∴sina=3/5

Similarly: sin(a+β)=63/65.

cosβ= cos[(a+β)-a]= cos(a+β)cosa+sin(a+β)Sina =(- 16/65)×(4/5)+(63/65)×(3/5)= 5/ 13