Question

prove sin(pi/4 +a).sin(pi/4 - a)=1/2cos2a

Answer 1

(Sinpi/4.cosa+cospi/4.sina).(Sinpi/4.cosa-cospi/4.sina)
=(1/√2.cosa+1/√2.sina)(1/√2.cosa-1/√2.sina)
=1/√2(Cosa+sina)1/√2(cosa-sina)
=1/2(cos²a-sin²a)
=1/2cos2a

Answer 2

Sin ( π/4 + x)sin(π/4-x) = 1/2 (2sin(45+x)sin(45-x). 1/2(cos(45+x-45+x)-cos(45+x+45-x). 1/2(cos 2x-cos 90). 1/2(cos2x-0).

1/2 cos 2x (proved)