Question

Find the value of sin 330º.cos 120° + cos 210ºsin 300​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

sin 330 = sin (360 - 30) = sin360cos30 - cos360sin30 = 0*cos30 - 1*1/2 = -1/2 ---(1)

Now, cos 120 = cos (90 + 30) = cos90cos30 - sin90sin30 = 0*cos30 - 1*1/2 = -1/2 ---(2)

Now cos210 = cos (180 + 30) = cos180cos30 - sin180sin30 = -1*√3/2 - 0*sin30 = -√3/2 ---(3)

sin 300 = sin (360 - 60) = sin360cos60 - cos360sin60 = 0*cos60 - 1* √3/2 = -√3/2 ---(4)

(1) × (2) + (3) × (4)

=> 1/4 + 3/4

= 4/4

=1.