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Tunjukkan bahwa: cos 50∘−cos 10∘sin 10∘−sin 50∘​=3​

Pertanyaan

Tunjukkan bahwa:

fraction numerator sin space 10 degree minus sin space 50 degree over denominator cos space 50 degree minus cos space 10 degree end fraction equals square root of 3

 

L. Nikmah

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

dapat ditunjukkan bahwa fraction numerator sin space 10 degree minus sin space 50 degree over denominator cos space 50 degree minus cos space 10 degree end fraction equals square root of 3.

Pembahasan

Ingat rumus jumlah dan selisih trigonometri berikut ini:

sin space A minus sin space B equals 2 space cos space 1 half open parentheses A plus B close parentheses space sin space 1 half open parentheses A minus B close parentheses

cos space A minus cos space B equals negative 2 space sin space 1 half open parentheses A plus B close parentheses space sin space 1 half open parentheses A minus B close parentheses

Dengan menggunakan konsep di atas, diperoleh hasil:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space 10 degree minus sin space 50 degree over denominator cos space 50 degree minus cos space 10 degree end fraction end cell equals cell fraction numerator 2 space cos space 1 half open parentheses 10 degree plus 50 degree close parentheses space sin space 1 half open parentheses 10 degree minus 50 degree close parentheses over denominator negative 2 space sin space 1 half open parentheses 50 degree plus 10 degree close parentheses space sin space 1 half open parentheses 50 degree minus 10 degree close parentheses end fraction end cell row blank equals cell negative fraction numerator space cos space 1 half open parentheses 60 degree close parentheses space sin space 1 half open parentheses negative 40 degree close parentheses over denominator sin space 1 half open parentheses 60 degree close parentheses space sin space 1 half open parentheses 40 degree close parentheses end fraction end cell row blank equals cell negative fraction numerator space cos space 30 degree space sin space open parentheses negative 20 degree close parentheses over denominator sin space 30 degree space sin space open parentheses 20 degree close parentheses end fraction end cell row blank equals cell negative fraction numerator space cos space 30 degree space open parentheses negative sin space 20 degree close parentheses over denominator sin space 30 degree space sin space open parentheses 20 degree close parentheses end fraction end cell row blank equals cell negative fraction numerator space cos space 30 degree space over denominator sin space 30 degree space end fraction times fraction numerator open parentheses negative sin space 20 degree close parentheses over denominator sin space open parentheses 20 degree close parentheses end fraction end cell row blank equals cell negative fraction numerator space cos space 30 degree space over denominator sin space 30 degree space end fraction times open parentheses negative 1 close parentheses end cell row blank equals cell fraction numerator space cos space 30 degree space over denominator sin space 30 degree space end fraction end cell row blank equals cell fraction numerator 1 half square root of 3 over denominator 1 half end fraction end cell row blank equals cell square root of 3 end cell end table

Jadi, dapat ditunjukkan bahwa fraction numerator sin space 10 degree minus sin space 50 degree over denominator cos space 50 degree minus cos space 10 degree end fraction equals square root of 3.

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