Pertanyaan

Jawablah dengan jelas dan benar. Hitunglah. csc 30 0 ∘ cot 15 0 ∘ × sec 24 0 ∘

Jawablah dengan jelas dan benar.

Hitunglah.

$\frac{cot 15 0 ^{\circ} \times sec 24 0 ^{\circ}}{csc 30 0 ^{\circ}}$

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

Maka,

$begin mathsize 14px style cot space 150 degree space equals space cot space open parentheses 180 space minus space 30 close parentheses degree space equals space minus cot space 30 degree space equals space fraction numerator 3 over denominator square root of 3 end fraction space equals space fraction numerator 3 square root of 3 over denominator 3 end fraction space equals space square root of 3 sec space 240 degree space equals space sec space open parentheses 180 space plus space 60 close parentheses degree space equals space minus sec space 60 degree space equals space minus 2 csc space 300 degree space equals space csc space open parentheses 360 space minus space 60 close parentheses degree space equals space minus csc space 60 degree space equals space fraction numerator 2 over denominator square root of 3 end fraction space equals space fraction numerator 2 square root of 3 over denominator 3 end fraction space equals space 2 over 3 square root of 3 end style$

Maka,

$begin mathsize 14px style fraction numerator cot space 150 degree space cross times space sec space 240 degree over denominator csc space 300 degree end fraction space equals space fraction numerator square root of 3 space cross times space left parenthesis negative 2 right parenthesis over denominator begin display style 2 over 3 end style square root of 3 end fraction space equals space minus fraction numerator 2 square root of 3 over denominator begin display style 2 over 3 end style square root of 3 end fraction space equals space minus 3 end style$