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Pertanyaan

begin mathsize 14px style fraction numerator 1 plus cos space straight pi over 6 over denominator cos space begin display style straight pi over 6 end style end fraction plus fraction numerator sin space begin display style straight pi over 6 end style over denominator 1 plus cos space begin display style straight pi over 6 end style end fraction equals... end style  

Pembahasan Soal:

Berdasarkan tabel trigonometri sudut istimewa begin mathsize 14px style cos space straight pi over 6 equals 1 half square root of 3 comma space dan space sin space straight pi over 6 equals 1 half end style, maka 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 plus cos space begin display style straight pi over 6 end style over denominator cos space begin display style straight pi over 6 end style end fraction plus fraction numerator sin space begin display style straight pi over 6 end style over denominator 1 plus cos space begin display style straight pi over 6 end style end fraction end cell equals cell fraction numerator 1 plus begin display style 1 half end style square root of 3 over denominator begin display style 1 half end style square root of 3 end fraction plus fraction numerator begin display style 1 half end style over denominator 1 plus begin display style 1 half end style square root of 3 end fraction end cell row blank equals cell fraction numerator open parentheses 1 plus 1 half square root of 3 close parentheses open parentheses 1 plus 1 half square root of 3 close parentheses plus open parentheses 1 half square root of 3 close parentheses open parentheses 1 half close parentheses over denominator open parentheses 1 half square root of 3 close parentheses open parentheses 1 plus 1 half square root of 3 close parentheses end fraction end cell row blank equals cell fraction numerator 1 plus begin display style 1 half end style square root of 3 plus begin display style 1 half end style square root of 3 plus begin display style 3 over 4 end style plus begin display style 1 fourth end style square root of 3 over denominator begin display style 1 half end style square root of 3 plus begin display style 3 over 4 end style end fraction end cell row blank equals cell fraction numerator open parentheses 1 plus begin display style 3 over 4 end style close parentheses plus open parentheses 1 half square root of 3 plus 1 half square root of 3 plus 1 fourth square root of 3 close parentheses over denominator 1 half square root of 3 plus 3 over 4 end fraction end cell row blank equals cell fraction numerator open parentheses 4 over 4 plus 3 over 4 close parentheses plus open parentheses 2 over 4 square root of 3 plus 2 over 4 square root of 3 plus 1 fourth square root of 3 close parentheses over denominator begin display style 2 over 4 end style square root of 3 plus begin display style 3 over 4 end style end fraction end cell row blank equals cell fraction numerator begin display style 7 over 4 end style plus begin display style 5 over 4 end style square root of 3 over denominator 2 over 4 square root of 3 plus 3 over 4 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 7 plus 5 square root of 3 over denominator 4 end fraction end style over denominator begin display style fraction numerator 3 plus 2 square root of 3 over denominator 4 end fraction end style end fraction end cell row blank equals cell fraction numerator 7 plus 5 square root of 3 over denominator 3 plus 2 square root of 3 end fraction end cell row blank equals cell fraction numerator 7 plus 5 square root of 3 over denominator 3 plus 2 square root of 3 end fraction cross times fraction numerator 3 minus 2 square root of 3 over denominator 3 minus 2 square root of 3 end fraction end cell row blank equals cell fraction numerator 21 minus 14 square root of 3 plus 15 square root of 3 minus 30 over denominator 9 minus 12 end fraction end cell row blank equals cell fraction numerator square root of 3 minus 9 over denominator negative 3 end fraction end cell row blank equals cell fraction numerator 9 minus square root of 3 over denominator 3 end fraction end cell end table end style  

Jadi  begin mathsize 14px style fraction numerator 1 plus cos space straight pi over 6 over denominator cos space begin display style straight pi over 6 end style end fraction plus fraction numerator sin space begin display style straight pi over 6 end style over denominator 1 plus cos space begin display style straight pi over 6 end style end fraction equals fraction numerator 9 minus square root of 3 over denominator 3 end fraction end style.  

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 14 Maret 2021

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