buktikan bahwa cos x - cos (x-120) - cos (x-240) = 2 cos x Tolong bantuin ya! makasii
Matematika
nrannisak
Pertanyaan
buktikan bahwa
cos x - cos (x-120) - cos (x-240) = 2 cos x
Tolong bantuin ya! makasii
cos x - cos (x-120) - cos (x-240) = 2 cos x
Tolong bantuin ya! makasii
2 Jawaban
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1. Jawaban vivaproducation
cos x + cos(x-120) + cos(x2-40) = 0
cosx + cosx.cos120 – sinx.sin120 + cosx.cos240 + sinx.sin240 = 0
cosx + cosx(-cos60)– sinx.sin60 + cosx.(-cos60) + sinx.(-sin60) = 0
cosx + cosx(-cos60) + cosx.(-cos60) - sinx.sin60 + sinx.(-sin60) = 0
cosx(1 – cos60 – cos60) – sinx(sin60 – sin60) = 0
cosx(1 – (1/2) – (1/2)) – sinx(½√3 - ½√3) = 0
(0)*cosx – (0)*sinx = 0
0 = 0 itu buktinyah kak -
2. Jawaban ahreumlim
Materi : Trigonometri
cos120
= cos(180-60)
= -cos60
= -1/2
cos240 = cos120
sin240 = -sin120
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cos x - cos (x-120) - cos (x-240)
= cosx - (cosx . cos120 + sinx . sin120) - (cosx . cos240 + sinx . sin240)
= cosx - cosx . cos120 - sinx . sin120 - cosx . cos240 - sinx . sin240
= cosx [1 - cos120 - cos240] - sinx [ sin120 + sin240]
= cosx [1 + 1/2 + 1/2]
= 2 cosx