Pertanyaan

cos 7 5 ∘ 1 − cos 1 5 ∘ 1 = ...

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

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Klaim

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

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Ingat bahwa $begin mathsize 14px style cos invisible function application straight alpha minus cos invisible function application straight beta equals negative 2 space sin invisible function application open parentheses fraction numerator straight alpha plus straight beta over denominator 2 end fraction close parentheses sin invisible function application open parentheses fraction numerator straight alpha minus straight beta over denominator 2 end fraction close parentheses end style$ 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 75 degree end fraction minus fraction numerator 1 over denominator cos invisible function application 15 degree end fraction space end cell equals cell fraction numerator cos invisible function application 15 degree minus cos invisible function application 75 degree over denominator cos invisible function application 75 degree cos invisible function application 15 degree end fraction space end cell row blank equals cell fraction numerator negative 2 space sin invisible function application begin display style left parenthesis fraction numerator 15 degree plus 75 degree over denominator 2 end fraction right parenthesis end style space sin invisible function application begin display style left parenthesis fraction numerator 15 degree minus 75 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 75 degree plus 15 degree right parenthesis plus cos invisible function application left parenthesis 75 degree minus 15 degree right parenthesis close parentheses end style end fraction space end cell row blank equals cell fraction numerator negative 2 space sin invisible function application begin display style left parenthesis fraction numerator 90 degree over denominator 2 end fraction right parenthesis end style space sin invisible function application begin display style left parenthesis fraction numerator negative 60 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 90 degree right parenthesis plus cos invisible function application left parenthesis 60 degree right parenthesis close parentheses end style end fraction end cell row blank equals cell fraction numerator negative 2 space sin invisible function application 45 degree space sin invisible function application begin display style left parenthesis negative 30 degree right parenthesis end style over denominator begin display style 1 half open parentheses cos invisible function application 90 degree plus cos invisible function application 60 degree close parentheses end style end fraction end cell row blank equals cell fraction numerator negative 4 space sin invisible function application 45 degree space sin invisible function application begin display style left parenthesis negative 30 degree right parenthesis end style over denominator begin display style cos invisible function application 90 degree plus cos invisible function application 60 degree end style end fraction end cell end table end style$

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