Question

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

Answer 1

see explanation

Explanation:

Using the product/ difference identity

sinxsiny =
`(1)/(2)` [ cos(x - y) - cos(x + y) ]

Consider the left side

2sin(
`(\pi )/(4)` + α)sin(
`(\pi )/(4)` - α )

= cos[
`(\pi )/(4)` + α -
`(\pi )/(4)` + α ] - cos [
`(\pi )/(4)` + α +
`(\pi )/(4)` - α ]

= cos2α - cos
`(\pi )/(2)`

= cos2α - 0

= cos2α = right side , thus proven