Sin780.sin120+cos240.sin390=1/2

1.	Sin780.sin120+cos240.sin390=1/2
Answer» ong>ANSWER: Sin780.sin120+cos240.sin390=1/2? Explanation: Prove that (1) SIN 780 sin 120 + cos 240 sin 390 = 1/2 (2) sin 600 cos 390+ cos 480 sin 150 = -1? sαṉḋÿ™ si12 years ago Favorite Answer 1)sin780.sin120+cos240.sin390 =sin(8x90+60).sin(90+30) +cos(3x90-30).sin(4x90+30) =sin60.cos30+[-sin30].sin30 =sin60.cos30 - sin30.sin30 =(root3)/2 x (root3)/2 -1/2 x1/2 =3/4 -1/4 =2/4 =1/2(PROVED) 2)sin600.cos390 + cos 480.sin150 =sin(6x90+60).cos(4x90+30) + cos(5x90+30)sin(90+60) =(-sin60).cos30 +-sin30.cos60 = -root3/2 x root3/2 +(-1/2 x 1/2) = -3/4-1/4 =-1(proved)...Show more

Answer»

ong>ANSWER:

Sin780.sin120+cos240.sin390=1/2?

Explanation:

Prove that (1) SIN 780 sin 120 + cos 240 sin 390 = 1/2 (2) sin 600 cos 390+ cos 480 sin 150 = -1?

sαṉḋÿ™

si12 years ago

Favorite Answer

1)sin780.sin120+cos240.sin390

=sin(8x90+60).sin(90+30) +cos(3x90-30).sin(4x90+30)

=sin60.cos30+[-sin30].sin30

=sin60.cos30 - sin30.sin30

=(root3)/2 x (root3)/2 -1/2 x1/2

=3/4 -1/4

=2/4

=1/2(PROVED)

2)sin600.cos390 + cos 480.sin150

=sin(6x90+60).cos(4x90+30) + cos(5x90+30)sin(90+60)

=(-sin60).cos30 +-sin30.cos60

= -root3/2 x root3/2 +(-1/2 x 1/2)

= -3/4-1/4

=-1(proved)...Show more

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