Pertanyaan

Nilai co t 10 5 ∘ tan 1 5 ∘ adalah....

Nilai $co t 10 5^{\circ} tan 1 5^{\circ}$ adalah....

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

Ingat! Sifat-sifat Trigonometri berikut: Maka:

Ingat!
Sifat-sifat Trigonometri berikut:

$begin mathsize 12px style c o t space alpha equals fraction numerator cos space alpha over denominator sin space alpha end fraction tan space alpha equals fraction numerator sin space alpha over denominator cos space alpha end fraction 2 space sin space alpha space cos space beta equals sin open parentheses alpha plus beta close parentheses plus sin open parentheses alpha minus beta close parentheses 2 space cos space alpha space sin space beta equals sin open parentheses alpha plus beta close parentheses minus sin open parentheses alpha minus beta close parentheses end style$

Maka:

$begin mathsize 12px style c o t space 105 degree space tan space 15 degree equals fraction numerator cos space 105 degree over denominator sin space 105 degree end fraction cross times fraction numerator sin space 15 degree over denominator cos space 15 degree end fraction c o t space 105 degree space tan space 15 degree equals fraction numerator begin display style 1 half end style open parentheses 2 space cos space 105 degree space sin space 15 degree close parentheses over denominator 1 half open parentheses 2 space sin space 105 degree space cos space 15 degree close parentheses end fraction c o t space 105 degree space tan space 15 degree equals fraction numerator begin display style sin open parentheses 105 degree plus 15 degree close parentheses minus sin open parentheses 105 degree minus 15 degree close parentheses end style over denominator sin open parentheses 105 degree plus 15 degree close parentheses plus sin open parentheses 105 degree minus 15 degree close parentheses end fraction c o t space 105 degree space tan space 15 degree equals fraction numerator begin display style sin space 120 degree minus sin space 90 degree end style over denominator sin space 120 degree plus sin space 90 degree end fraction c o t space 105 degree space tan space 15 degree equals fraction numerator begin display style 1 half square root of 3 minus 1 end style over denominator 1 half square root of 3 plus 1 end fraction space open parentheses semua space dikalikan space dengan space 2 over 2 close parentheses c o t space 105 degree space tan space 15 degree equals fraction numerator begin display style square root of 3 minus 2 end style over denominator square root of 3 plus 2 end fraction space open parentheses selanjutnya space dirasionalkan close parentheses c o t space 105 degree space tan space 15 degree equals fraction numerator begin display style square root of 3 minus 2 end style over denominator square root of 3 plus 2 end fraction cross times fraction numerator begin display style square root of 3 minus 2 end style over denominator square root of 3 minus 2 end fraction c o t space 105 degree space tan space 15 degree equals fraction numerator begin display style 3 minus 2 square root of 3 minus 2 square root of 3 plus 4 end style over denominator 3 minus 4 end fraction c o t space 105 degree space tan space 15 degree equals negative 7 plus 4 square root of 3 end style$