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Tunjukkanlah bahwa : sin 22 , 5 ∘ cos 22 , 5 ∘ − cos 2 22 , 5 ∘ = − 2 1 ​

Tunjukkanlah bahwa :    

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N. Sari

Master Teacher

Mahasiswa/Alumni Universitas Nasional

Jawaban terverifikasi

Pembahasan

Sifat penjumlahan dan pengurangan trigonometri : Sifat perkalian trigonometri : Dengan menggunakan sifat tersebut, maka : Maka terbukti bahwa .

Sifat penjumlahan dan pengurangan trigonometri :

sin space straight A plus sin space straight B equals 2 sin 1 half left parenthesis straight A plus straight B right parenthesis cos 1 half left parenthesis straight A minus straight B right parenthesis sin space straight A minus sin space straight B equals 2 cos 1 half left parenthesis straight A plus straight B right parenthesis sin 1 half left parenthesis straight A minus straight B right parenthesis cos space straight A plus cos space straight B equals 2 cos 1 half left parenthesis straight A plus straight B right parenthesis cos 1 half left parenthesis straight A minus straight B right parenthesis cos space straight A minus cos space straight B equals 2 sin 1 half left parenthesis straight A plus straight B right parenthesis sin 1 half left parenthesis straight A minus straight B right parenthesis 

Sifat perkalian trigonometri :

2 sin space straight A space cos space straight B equals sin left parenthesis straight A plus straight B right parenthesis plus sin left parenthesis straight A minus straight B right parenthesis 2 cos space straight A space sin space straight B equals sin left parenthesis straight A plus straight B right parenthesis minus sin left parenthesis straight A minus straight B right parenthesis 2 cos space straight A space cos space straight B equals cos left parenthesis straight A plus straight B right parenthesis plus cos left parenthesis straight A minus straight B right parenthesis minus 2 sin space straight A space sin space straight B equals cos left parenthesis straight A plus straight B right parenthesis plus cos left parenthesis straight A minus straight B right parenthesis 

Dengan menggunakan sifat tersebut, maka :

sin space 22 comma 5 degree cos space 22 comma 5 degree minus cos squared space 22 comma 5 degree equals 1 half open parentheses 2 sin space 22 comma 5 degree cos space 22 comma 5 degree close parentheses minus 1 half open parentheses 2 cos squared space 22 comma 5 degree close parentheses equals 1 half open parentheses sin space 45 degree close parentheses minus 1 half open parentheses 2 space cos space 22 comma 5 degree cos space 22 comma 5 degree close parentheses equals 1 half cross times 1 half square root of 2 minus 1 half open parentheses cos space 45 degree plus 1 close parentheses equals 1 half cross times 1 half square root of 2 minus 1 half cross times 1 half square root of 2 minus 1 half equals negative 1 half  

Maka terbukti bahwa sin space 22 comma 5 degree cos space 22 comma 5 degree minus cos squared space 22 comma 5 degree equals negative 1 half

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