Sin780.sin120+cos240.sin390=1/2
Answers
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
Explanation:
LHS=sin780.sin120+cos240.cos390
=sin(360*2+60).sin(360+30)+cos(360-120).cos(360+30)
=sin60.sin60-cos120.sin30 (keep in mind degree,i have skip it for easiness)
=sqrt3/2.sqrt3/2-1/2.1/2
=3/4-1/4
=2/4=1/2=RHS
hence proved