Answer:
see explanation
Step-by-step explanation:
Using the product/ difference identity
sinxsiny = [tex]\frac{1}{2}[/tex] [ cos(x - y) - cos(x + y) ]
Consider the left side
2sin([tex]\frac{\pi }{4}[/tex] + α)sin([tex]\frac{\pi }{4}[/tex] - α )
= cos[[tex]\frac{\pi }{4}[/tex] + α - [tex]\frac{\pi }{4}[/tex] + α ] - cos [[tex]\frac{\pi }{4}[/tex] + α + [tex]\frac{\pi }{4}[/tex] - α ]
= cos2α - cos[tex]\frac{\pi }{2}[/tex]
= cos2α - 0
= cos2α = right side , thus proven
