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Tentukan hasil dari cos 31 5 ∘ sin 12 0 ∘ + tan 24 0 ∘ = ...

Tentukan hasil dari $\frac{sin 12 0 ^{\circ} + tan 24 0 ^{\circ}}{cos 31 5 ^{\circ}} = ...$

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Jawaban terverifikasi

Jawaban

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$fraction numerator sin 120 degree plus tan 240 degree over denominator cos 315 degree end fraction equals 3 over 2 square root of 6$ .

Pembahasan

Kita ingat sudut berelasi di kuadran II, III, dan IV. serta ingat nilai trigonometri sudut istimewa, Jadi, .

Kita ingat sudut berelasi di kuadran II, III, dan IV. serta ingat nilai trigonometri sudut istimewa,

$fraction numerator sin 120 degree plus tan 240 degree over denominator cos 315 degree end fraction equals fraction numerator sin open parentheses 180 degree minus 60 degree close parentheses plus tan open parentheses 180 degree plus 60 degree close parentheses over denominator cos open parentheses 360 degree minus 45 degree close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator sin 60 degree plus tan 60 degree over denominator cos 45 degree end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 1 half square root of 3 plus square root of 3 over denominator 1 half square root of 2 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 3 over 2 square root of 3 over denominator 1 half square root of 2 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 3 square root of 3 over denominator square root of 2 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 3 square root of 3 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 3 square root of 6 over denominator 2 end fraction$

Jadi, $fraction numerator sin 120 degree plus tan 240 degree over denominator cos 315 degree end fraction equals 3 over 2 square root of 6$ .