Question

Use the sum-to-product formulas to write the given expression as a product
sin8θ-sin6θ

Answer 1

i dont have these memorized

http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Product-to-sum_and_sum-to-product_identities

Answer 2

here you have the basic sum-to-product formula that goes as follows :
sin(x)+sin(y) = 2sin[(x+y)/2]cos[(x-y)/2]
since you have sin(x)-sin(y) the (x+y) and the (x-y) change from sine to cosine and vice-versa, giving :

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

apply this to the given expression :

sin8θ-sin6θ=2cos[(8θ+6θ)/2]sin[(8θ-6θ)/2]
=2cos(14θ/2)sin(2θ/2)
=2cos7θsinθ

Answer 3

btw I stress on learning the tricks of the trade when working with trigonometry, these exercises will pave your way to differentials wich will be easy as peeling a banana when you understand the concepts of trigonometry...