Question

Question #9e27a

Answer 1

Regardless of the unit you use for the angle, the following relations hold:

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

(you can check them out here )

You only need to recognize the right case:
`\sin(45)\cos(15) + \cos(45)\sin(15)` is an expression of the form `\sin(a)\cos(b) + \cos(b)\sin(a)`, which is the sine of the sum of the angles, so
`\sin(45)\cos(15) + \cos(45)\sin(15)=\sin(45+15)=\sin(60)=\sqrt(3)/2`