Question

Please help if you can, I do not understand Trig at all.
Question: Complete the left-hand column of the table below following the steps indicated in the right-hand column to show that sin(a) sin (b)= 1/2 [cos (a-b)-cos (a+b)] is an identity. Use the definitions of sum and difference formulas for cosine.
*the left hand column that I need to fill out is labeled "Calculations" while the right-hand column that is labeled "Reason" goes as followed:
1. Given on the right side of the original equation.
2. Apply the definitions of the sum and difference identities for cosine.
3. Simplify the e

Answer 1

3. Simplify the expression.

Answer 2

then some algebra to simplify the right hand side. i.e. distribute and combine like terms, and you would get the left hand side

Answer 3

\[\sin(a)\cos(b)=\\\frac{1}{2}(\overbrace{\cos(a)\cos(b)+\sin(a)\sin(b}^{\text{subtraction form for cosine}}))-(\overbrace{\cos(a)\cos(b)-\sin(a)\sin(b)}^{\text{addition form for cosine}})\]

Answer 4

Oh, okay. I will try that, thank you. :)

Answer 5

yw

Answer 6

@satellite73 would the end result after simplifying the expression be: -cos(a) cos(b)/2 + sin(a) sin(b)/2 + sin(a) sin(b)? That's what I got.