Question

How do you use the product to sum formulas to write `sin(x+y)sin(x-y)` as a sum or difference?

Answer 1

`sin(x+y)sin(x-y)=1/2[cos2y-cos2x]`

Explanation:

We can use the product to sum formula

`sinAsinB=1/2[cos(A-B)-cos(A+B)]`

Hence `sin(x+y)sin(x-y)`

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

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

= `1/2[cos2y-cos2x]`