Pertanyaan

cos 22 5 ∘ ⋅ sin 4 5 ∘ ⋅ cotan 25 0 ∘ sin 30 0 ∘ ⋅ cos 5 0 ∘ ⋅ tan 16 0 ∘ = ...

$\frac{sin 30 0 ^{\circ} \cdot cos 5 0 ^{\circ} \cdot tan 16 0 ^{\circ}}{cos 22 5 ^{\circ} \cdot sin 4 5 ^{\circ} \cdot cotan 25 0 ^{\circ}} = ...$

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

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$fraction numerator sin space 300 degree times cos space 50 degree times tan space 160 degree over denominator cos space 225 degree times sin space 45 degree times cotan space 250 degree end fraction equals negative 1 half square root of 3$ .

Pembahasan

Dengan menggunakan rumus sudut berelasi, diperoleh Jadi, .

Dengan menggunakan rumus sudut berelasi, diperoleh

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space 300 degree times cos space 50 degree times tan space 160 degree over denominator cos space 225 degree times sin space 40 degree times cotan space 250 degree end fraction end cell row blank equals cell fraction numerator sin space 300 degree times cos space open parentheses 90 minus 40 close parentheses degree times tan space open parentheses 90 plus 70 close parentheses degree over denominator cos space 225 degree times sin space 40 degree times cotan space open parentheses 180 plus 70 close parentheses degree end fraction end cell row blank equals cell fraction numerator sin space 300 degree times sin space 40 degree times open parentheses negative cotan space 70 degree close parentheses over denominator cos space 225 degree times sin space 40 degree times cotan space 70 degree end fraction end cell row blank equals cell negative fraction numerator sin space 300 degree over denominator cos space 225 end fraction end cell row blank equals cell negative fraction numerator negative begin display style 1 half end style square root of 3 over denominator negative begin display style 1 half end style square root of 2 end fraction end cell row blank equals cell negative fraction numerator square root of 3 over denominator square root of 2 end fraction end cell row blank equals cell negative 1 half square root of 3 end cell end table$

Jadi, $fraction numerator sin space 300 degree times cos space 50 degree times tan space 160 degree over denominator cos space 225 degree times sin space 45 degree times cotan space 250 degree end fraction equals negative 1 half square root of 3$ .