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Buktikan identitas trigonometri berikut. b.  1+sinβcos β​=cos β1−sinβ​

Pertanyaan

Buktikan identitas trigonometri berikut.

b.  fraction numerator cos space beta over denominator 1 plus sin beta end fraction equals fraction numerator 1 minus sin beta over denominator cos space beta end fraction

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

terbukti bahwa table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator cos space beta over denominator 1 plus sin beta end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 minus sin beta over denominator cos space beta end fraction end cell end table.

Pembahasan

Ingat!

  • sin squared beta plus cos squared beta equals 1 seshingga cos squared beta equals 1 minus sin squared beta

Akan dibuktikan

fraction numerator cos space beta over denominator 1 plus sin beta end fraction equals fraction numerator 1 minus sin beta over denominator cos space beta end fraction

Perhatikan perhitungan berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cos space beta over denominator 1 plus sin beta end fraction end cell equals cell fraction numerator cos space beta over denominator 1 plus sin beta end fraction cross times fraction numerator 1 minus sin beta over denominator 1 minus sin beta end fraction end cell row blank equals cell fraction numerator cos space beta open parentheses 1 minus sin beta close parentheses over denominator 1 minus sin squared beta end fraction end cell row blank equals cell fraction numerator cos space beta open parentheses 1 minus sin beta close parentheses over denominator 1 minus sin squared beta end fraction end cell row blank equals cell fraction numerator cos space beta open parentheses 1 minus sin beta close parentheses over denominator cos squared space beta end fraction end cell row blank equals cell fraction numerator up diagonal strike cos space beta end strike open parentheses 1 minus sin beta close parentheses over denominator up diagonal strike cos space beta end strike times cos space beta end fraction end cell row blank equals cell fraction numerator 1 minus sin beta over denominator cos space beta end fraction end cell end table

Dengan demikian terbukti bahwa table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator cos space beta over denominator 1 plus sin beta end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 minus sin beta over denominator cos space beta end fraction end cell end table.

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