Question

Hello , anyone able to help with question 5? thanks :)!

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the product/ difference identity

sinxsiny = $\frac{1}{2}$ [ cos(x - y) - cos(x + y) ]

Consider the left side

2sin($\frac{\pi }{4}$ + α)sin($\frac{\pi }{4}$ - α )

= cos[$\frac{\pi }{4}$ + α - $\frac{\pi }{4}$ + α ] - cos [$\frac{\pi }{4}$ + α + $\frac{\pi }{4}$ - α ]

= cos2α - cos$\frac{\pi }{2}$

= cos2α - 0

= cos2α = right side , thus proven