Question

Which of the following expressions does sin(x − y) − sin(x + y) simplify to?−2(cos x)(cos y)−2(cos x)(sin y)−2(sin x)(sin y)−2(sin x)(cos y)

Answer 1

we have the expression

sin(x − y) − sin(x + y)

Remember that

sin(x-y)=sinxcosy-cosxsiny

and

sin(x+y)=sinxcosy+cosxsiny

Substitute in the given expression

sinxcosy-cosxsiny-[sinxcosy+cosxsiny]

Remove the parenthesis

sinxcosy-cosxsiny-sinxcosy-cosxsiny

Combine like terms

-2cosxsiny

therefore

The answer is

−2(cos x)(sin y)