Question

$\sin(a) + \sin(b) = 2 \: \\ prove \: that \: \cos(a - b) = 1$

Answer 1

sin a + sin b = 2
sin a + sin b = sin 90 + sin 90 or 2(sin 90)
so a + b = 180 degree
a = 180- b.....eq 1
cos (180- b -b) = cos 0
180-2b = 0
-2b = -180
b = 90