Question

Prove that cos570°sin510° + sin(-330°)cos(-390) = 0​

Answer 1

Answer:

Please see the attachment

Answer 2

Answer:

Formula used

$\cos( - x) = \cos(x) \\ \sin( - x) = - \sin(x) \\ \cos(450 + x) = - \sin(x) \\ \cos(360 + x) = \cos(x) \\ sin(360 - x) = - \sin(x)$

Use Cartesian to remember signs.

$\cos(570) \sin(510) + \sin( - 330) \cos( - 390) \\ = \cos(450 + 120) \sin(450 + 60) - \sin(360 - 30) \cos(360 + 30) \\ = \sin(120) \sin(60) - ( \sin(30) ) \cos(30) ) \\ = \cos(60) \sin(60) - \cos(30) \sin(30) \\ = \sin(90 - 60) \cos(90 - 60) - \sin(30) \cos(30) \\ = \sin(30) \cos(30) - \sin(30) \cos(30) \\ = 0$