Question

How do you evaluate `sin((5pi)/9)cos((7pi)/18)-cos((5pi)/9)sin((7pi)/18)`?

Answer 1

`1/2`

Explanation:

This equation can be solved using some knowledge about some trigonometric identities. In this case, the expansion of `sin(A-B)` should be known:

`sin(A-B)=sinAcosB-cosAsinB`

You'll notice that this looks awfully similar to the equation in the question. Using the knowledge, we can solve it:
`sin((5pi)/9)cos((7pi)/18)-cos((5pi)/9)sin((7pi)/18)`
`=sin((5pi)/9-(7pi)/18)`
`=sin((10pi)/18-(7pi)/18)`
`=sin((3pi)/18)`
`=sin((pi)/6)`, and that has exact value of `1/2`