compute sin(38)+sin(7)

Question

it says the answer is √2sin(31) but I'm confused on how they got the root 2

Answer 1

sinA+SinB = 2[sin[(A+B)/2]cos[(A-B)/2]]

sin38+ sin7 = 2sin((38+7)/2)cos((38-7)/2)

= 2sin(45/2)cos(31/2)

= 2sin22.5cos15.5= about .7375

sqr2sin31 = about .7283