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Tunjukkan bahwa: cos 3∘+cos 33∘sin 3∘+sin 33∘​=tan 18∘

Pertanyaan

Tunjukkan bahwa:

fraction numerator sin space 3 degree plus sin space 33 degree over denominator cos space 3 degree plus cos space 33 degree end fraction equals tan space 18 degree

 

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

dapat ditunjukkan bahwa fraction numerator sin space 3 degree plus sin space 33 degree over denominator cos space 3 degree plus cos space 33 degree end fraction equals tan space 18 degree.

Pembahasan

Ingat rumus jumlah dan selisih trigonometri berikut ini:

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

cos space A plus cos space B equals 2 space cos space 1 half open parentheses A plus B close parentheses space cos 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 3 degree plus sin space 33 degree over denominator cos space 3 degree plus cos space 33 degree end fraction end cell equals cell fraction numerator 2 space sin space 1 half open parentheses 3 degree plus 33 degree close parentheses space cos space 1 half open parentheses 3 degree minus 33 degree close parentheses over denominator 2 space cos space 1 half open parentheses 3 degree plus 33 degree close parentheses space cos space 1 half open parentheses 3 degree minus 33 degree close parentheses end fraction end cell row blank equals cell fraction numerator sin space 1 half open parentheses 36 degree close parentheses over denominator cos space 1 half open parentheses 36 degree close parentheses end fraction times fraction numerator cos space 1 half open parentheses negative 30 degree close parentheses over denominator cos space 1 half open parentheses negative 30 degree close parentheses end fraction end cell row blank equals cell fraction numerator sin space 18 degree over denominator cos space 18 degree end fraction times fraction numerator cos space open parentheses negative 15 degree close parentheses over denominator cos space open parentheses negative 15 degree close parentheses end fraction end cell row blank equals cell fraction numerator sin space 18 degree over denominator cos space 18 degree end fraction.1 end cell row blank equals cell tan space 18 degree end cell end table

Jadi, dapat ditunjukkan bahwa fraction numerator sin space 3 degree plus sin space 33 degree over denominator cos space 3 degree plus cos space 33 degree end fraction equals tan space 18 degree.

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