Question

Find the value of sin 330° . cos 120° + cos 120° . sin 300°.

Answer 1

Answer:

          (1+root 3)/4

Step-by-step explanation:

sin 330 = sin (360-30)

             =  - sin 30

            = -1/2

cos 120 = cos (90+30)

            = -sin 30

           = -1/2

sin 300 = sin (270+30)

             = -cos 30

           = -root 3/2

so ,  sin 300*cos 120+cos 120*sin 300 = (-1/2*-1/2) + (-1/2*-root3/2)

                                                                 = (1+root 3)/4

Answer 2

Solution :

i ) sin330°

= sin( 360° - 30° )

= - sin 30°

= -1/2

ii ) cos 120°

= cos ( 90° + 30° )

= - sin 30°

= -1/2

iii ) cos 210°

= cos ( 180° + 30° )

= - cos 30°

= - √3/2

iv ) sin 300°

= sin ( 270° + 30° )

= - cos 30°

= -√3/2

Now ,

sin 330°.cos 120°+cos210°.sin 300°

= ( -1/2 ) ( -1/2 ) + ( -√3/2 )( -√3/2 )

= 1/4 + 3/4

= ( 4/4 )

= 1

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