Question

cos420 sin(-300)-sin870 cos570

Answer 1

$\cos(420) = \cos(360 + 60 ) = \cos(60)$
$\sin( - 300) = - \sin(300) = \sin(360 - 60) = \sin(60)$
$\sin(870) = \sin(360 \times 2 + 150 ) = \sin(150) = \sin(90 + 60) = \cos(60)$
$\cos(570) = \cos(360 +210 ) = \cos(210) = \cos(180 + 30) = - \cos(30)$
cos420.sin(-300)-sin870.cos570=cos60.sin60 + cos60.cos30 =2sin60.cos60= sin120=√3/2 ( because cos30= cos(90-60) = sin60 )

Answer 2

Answer:

$\sqrt{3 \div 2}$