I'm really confused on how to do this. Can someone show me step by step on how to solve this? The directions say to use the Sum-to-Product formulas to find the exact value of the expression.

Question

sin 5pi/4-sin 3pi/4

Answer 1

you want to use these identities
http://www.mathwords.com/s/sum_to_product_identities.htm

especially this one
sinx - siny = 2cos( (x+y)/2 )sin(( x-y)/2 )

sin 5π/4 - sin3π/4
= 2cos(π)sin(π/4)
= 2(-1)(√2/2)
= -√2