Question

The value of sin 150° cos 120° + cos 330° sin 660° is ______.

Options

• – 3

• – 2

• – 1

• 0

Answer 1

The value of sin 150° cos 120° + cos 330° sin 660° is – 1.

Explanation:

LHS = sin 150° cos 120° + cos 330° sin 660° 

= sin(90° + 60°) cos(180° – 60°) + cos(360° – 30°) sin(2 × 360° – 60°)

= cos 60° (– cos 60°) + (cos 30°) (– sin 60°)

= `1/2 . (- 1/2) + sqrt(3)/2 . (- sqrt(3)/2)`

= `- 1/4 - 3/4`

= – 1