Question

If SINA=4/5 And COSB=5/13 find COS(A-B/2)

Answer 1

sinA=4/5
sin²A+cos²A=1
(4/5)²+cos²A=1
cos²A=1-16/25
cos²A=25-16/25
cos²A=9/25
cosA=3/5
cos(A-B/2)=(3/5-5/13/2)
=39-25/65/2
=14/65/2
=14×2/65
=28/65