Pertanyaan

cos 16 5 ∘ 1 + cos 7 5 ∘ 1 = ....

$\frac{1}{cos 16 5 ^{\circ}} + \frac{1}{cos 7 5 ^{\circ}} = ....$

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Klaim

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Perhatikan bahwa : Ingat bahwa dan . Sehingga : Ingat bahwa dan . Sehingga :

Perhatikan bahwa :

Ingat bahwa $begin mathsize 14px style cos invisible function application straight alpha plus cos invisible function application straight beta equals 2 space cos invisible function application open parentheses fraction numerator straight alpha plus straight beta over denominator 2 end fraction close parentheses cos invisible function application open parentheses fraction numerator straight alpha minus straight beta over denominator 2 end fraction close parentheses end style$ dan . Sehingga :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 over denominator cos invisible function application 165 degree end fraction plus fraction numerator 1 over denominator cos invisible function application 75 degree end fraction space end cell equals cell fraction numerator cos invisible function application 75 degree plus cos invisible function application 165 degree over denominator cos invisible function application 165 degree cos invisible function application 75 degree end fraction space end cell row blank equals cell fraction numerator 2 space cos invisible function application begin display style left parenthesis fraction numerator 75 degree plus 165 degree over denominator 2 end fraction right parenthesis end style space cos invisible function application begin display style left parenthesis fraction numerator 75 degree minus 165 degree over denominator 2 end fraction right parenthesis end style over denominator begin display style 1 half space open parentheses cos invisible function application left parenthesis 165 degree plus 75 degree right parenthesis plus cos invisible function application left parenthesis 165 degree minus 75 degree right parenthesis close parentheses end style end fraction space end cell row blank equals cell fraction numerator 2 space cos invisible function application begin display style left parenthesis fraction numerator 240 degree over denominator 2 end fraction right parenthesis end style space cos invisible function application begin display style left parenthesis fraction numerator negative 90 degree over denominator 2 end fraction right parenthesis end style over denominator begin display style 1 half space open parentheses cos invisible function application left parenthesis 240 degree right parenthesis plus cos invisible function application left parenthesis 90 degree right parenthesis close parentheses end style end fraction end cell row blank equals cell fraction numerator 2 space cos invisible function application 120 degree space cos invisible function application begin display style left parenthesis negative 45 degree right parenthesis end style over denominator begin display style 1 half open parentheses cos invisible function application 240 degree plus cos invisible function application 90 degree close parentheses end style end fraction end cell row blank equals cell fraction numerator 2 space cos invisible function application 120 degree space cos invisible function application begin display style left parenthesis negative 45 degree right parenthesis end style over denominator begin display style cos invisible function application 240 degree plus cos invisible function application 90 degree end style end fraction end cell end table end style$

Ingat bahwa dan . Sehingga :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 over denominator cos invisible function application 165 degree end fraction space plus fraction numerator 1 over denominator cos invisible function application 75 degree end fraction space end cell equals cell fraction numerator 4 space cos invisible function application 120 degree space space cos invisible function application left parenthesis negative 45 degree right parenthesis over denominator cos invisible function application 240 degree plus cos invisible function application 90 degree end fraction end cell row blank equals cell fraction numerator 4 space cos invisible function application left parenthesis 180 degree minus 60 degree right parenthesis space space cos invisible function application left parenthesis negative 45 degree right parenthesis over denominator cos invisible function application left parenthesis 180 degree plus 60 degree right parenthesis plus cos invisible function application 90 degree end fraction space end cell row blank equals cell fraction numerator 4 left parenthesis negative cos invisible function application 60 degree space right parenthesis space space cos invisible function application 45 degree over denominator negative cos invisible function application 60 degree plus cos invisible function application 90 degree end fraction end cell row blank equals cell fraction numerator 4 open parentheses negative begin display style 1 half end style close parentheses open parentheses begin display style 1 half end style square root of 2 close parentheses over denominator open parentheses negative begin display style 1 half end style plus 0 close parentheses end fraction end cell row blank equals cell fraction numerator negative square root of 2 over denominator negative begin display style 1 half end style end fraction end cell row blank equals cell 2 square root of 2 end cell end table end style$