BuktikanSin (α + 45 ) + sin ( α – 45 ) = akar 2 sin α

Sin A + sin B =2.sin [(A + B)/2].cos [(A-B)/2]
A = a + 45
B = a – 45

Maka
Sin (a+45) + sin (a-45)
= 2.sin [(a+45+a-45)/2].cos[(a+45-(a-45)]/2
= 2.sin [(2a)/2].cos [90/2]
= 2.sin a.cos 45
=2.sin a.(akar 2)/2
= sin a. Akar2 atau akar 2. Sin a (terbukti)