Sederhanakanlah 1/2 cos (1/4 phi+alpha)sin(1/4 phi-alpha)?

jawab

 2 cos A sin B= sin (A+B) - sin (A-B)

1/2 cos(1/4 π + a) sin (1/4π- a) = 
= 1/4 { 2 cos(1/4π + a) sin (1/4 π- a )}
= 1/4 { sin(1/4 π+a + 1/4 π - a) - sin (1/4 π+a - 1/4π + a)}
= 1/4 (sin 1/2 π - sin 2a)
= 1/4 (1- sin 2a)
= 1/4 - 1/4 sin 2a