Half And Double angle and adding/subtracting trig identities

Sinα = 4/5 and Cosβ = 5/13

Sin2α
Cos2α
Sinαβ
Tan2α
Cos1/2β
Tan1/2α
Sin1/2α
Can You Please show me how to do this practice problems step by step!! :) i have a test on this tomorrow and can seem to understand these!! :/ I would really appreciate it :D

sinA = 4/5, the other side has to be 3.

sin(2A)
= 2sinAcosA
= 2(4/5)(3/5)
= 24/25

cos(2A)
= cos^2(A) - sin^2(A)
= (3/5)^2 - (4/5)^2
= 9/25 - 16/25
= -7/25

tan(2A)
= sin(2A)/cos(2A)
= 24/-7
= -24/7