Question

sin 120° cos 150° – cos 240° sin 330° is equal to

(a) \(-\bigg(\frac{\sqrt3+1}{4}\bigg)\)

(b) –1 

c) 1 

(d) \(\frac23\)

Answer 1

(b)  -1 

sin 120° cos 150° – cos 240° sin 330° 

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

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

= \(\frac{\sqrt3}{2}\times-\frac{\sqrt3}{2}-\big(\frac{-1}{2}\big)\big(\frac{-1}{2}\big)\) = \(-\frac34-\frac14=-\frac44=-1.\)