Question

show that sin600∘ cos330 ∘ + cos120 ∘ sin150 ∘ = −1​

Answer 1

sin (360°+240°) cos (360°-30°)+cos (90°+30°)sin (180°-30°)

sin 240° cos 30° -sin 30° sin30°

sin (270°-30°) cos 30° -(1/2)(1/2)

-cos30°cos 30°-1/4

-(√3/2)(√3/2)-1/4

-3/4-1/4

-4/4

-1

hence proved