How do i give the exact value for:

Question

(sin pi/8)(cos pi/24) + (cos pi/8)(sin pi/24)

Answer 1

recall that
sin(A+B) = sinAcosB + cosAsinB

you have the same angle pair showing up in the two terms in that pattern, so
(sin pi/8)(cos pi/24) + (cos pi/8)(sin pi/24)
= sin(pi/8 + pi/24)
= sin(pi/6)
= 1/2 ----> you should know pi/6 =30 degrees and sin(30) = 1/2