Pertanyaan

Nilai dari cos 22 5 ∘ + cos 1 5 ∘ sin 22 5 ∘ + sin 1 5 ∘ = ...

Nilai dari $\frac{sin 22 5 ^{\circ} + sin 1 5 ^{\circ}}{cos 22 5 ^{\circ} + cos 1 5 ^{\circ}} = ...$

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

$begin mathsize 14px style fraction numerator sin space 225 degree plus sin space 15 degree over denominator cos space 225 degree plus cos space 15 degree end fraction equals negative square root of 3 end style$

Pembahasan

Dengan menggunakan rumus penjumlahan dua sinus dan penjumlahan dua cosinus diperoleh Jadi

Dengan menggunakan rumus penjumlahan dua sinus dan penjumlahan dua cosinus diperoleh

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space 225 degree plus sin space 15 degree over denominator c o s space 225 degree plus cos space 15 degree end fraction end cell equals cell fraction numerator 2 times sin begin display style 1 half end style left parenthesis 225 degree plus 15 degree right parenthesis times cos begin display style 1 half end style left parenthesis 225 degree minus 15 degree right parenthesis over denominator 2 times cos space begin display style 1 half end style left parenthesis 225 degree plus 15 degree right parenthesis times cos space begin display style 1 half end style left parenthesis 225 degree minus 15 degree right parenthesis end fraction end cell row blank equals cell fraction numerator 2 times sin space 120 degree times cos space 105 degree over denominator 2 times cos space 120 degree times cos space 105 degree end fraction end cell row blank equals cell fraction numerator 2 times sin space 120 degree over denominator 2 times cos space 120 degree end fraction end cell row blank equals cell fraction numerator 2 times begin display style 1 half end style square root of 3 over denominator 2 times left parenthesis negative begin display style 1 half end style right parenthesis end fraction end cell row blank equals cell fraction numerator square root of 3 over denominator negative 1 end fraction end cell row blank equals cell negative square root of 3 end cell end table end style$

Jadi $begin mathsize 14px style fraction numerator sin space 225 degree plus sin space 15 degree over denominator cos space 225 degree plus cos space 15 degree end fraction equals negative square root of 3 end style$