Use a sum or difference formula to find the exact value of the following. sin(13\pi)/(28)cos(2\pi)/(7)+cos(13\pi)/(28)sin(2\pi)/(7)

Question

Use a sum or difference formula to find the exact value of the following.


`sin(13\pi)/(28)cos(2\pi)/(7)+cos(13\pi)/(28)sin(2\pi)/(7)`

Answer 1

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Answer 2

You can see that your expression is in the form

`\sin(a)\cos(b) + \cos(a)\sin(b)`

By the sine sum formula, this is the same as
`\sin(a+b)`

Since in your case

`a = \cfrac{13\pi}{28},\quad b = \cfrac{2\pi}{7}`

your expression evaluates to

`\sin\left(\cfrac{13\pi}{28} + \cfrac{2\pi}{7}\right) = \sin\left(\cfrac{3\pi}{4} \right) = \cfrac{1}{√(2)} = \cfrac{√(2)}{2}`