Latihan Matematika Peminatan Kelas XI Jumlah, Selisih, dan Perkalian Sinus dan Cosinus
# 3
Pilgan

cos⁡32°cos⁡18°\cos32\degree\cos18\degree dapat ditulis menjadi ....

A

12(cos⁡(14°)+cos⁡(50°))\frac{1}{2}\left(\cos\left(14\degree\right)+\cos\left(50\degree\right)\right)

B

12(cos⁡(32°)+cos⁡(18°))\frac{1}{2}\left(\cos\left(32\degree\right)+\cos\left(18\degree\right)\right)

C

12(sin⁡(14°)+sin⁡(50°))\frac{1}{2}\left(\sin\left(14\degree\right)+\sin\left(50\degree\right)\right)

D

12(sin⁡(32°)+sin⁡(18°))\frac{1}{2}\left(\sin\left(32\degree\right)+\sin\left(18\degree\right)\right)

E

12(cos⁡(32°)+sin⁡(18°))\frac{1}{2}\left(\cos\left(32\degree\right)+\sin\left(18\degree\right)\right)

Pembahasan:

Rumus umum perkalian cosinus adalah

cos⁡αcos⁡β=12(cos⁡(α−β)+cos⁡(α+β))\cos\alpha\cos\beta=\frac{1}{2}\left(\cos\left(\alpha-\beta\right)+\cos\left(\alpha+\beta\right)\right)

Dengan demikian,

cos⁡32°cos⁡18°=12(cos⁡(32°−18°)+cos⁡(32°+18°))\cos32\degree\cos18\degree=\frac{1}{2}\left(\cos\left(32\degree-18\degree\right)+\cos\left(32\degree+18\degree\right)\right)

=12(cos⁡(14°)+cos⁡(50°))=\frac{1}{2}\left(\cos\left(14\degree\right)+\cos\left(50\degree\right)\right)

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