Pertanyaan

tan 13 5 ∘ + tan 1 5 ∘ = ...

$tan 13 5^{\circ} + tan 1 5^{\circ} =$ ...

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Habis dalam

Klaim

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

tan space 135 degree plus tan space 15 degree equals 1 minus square root of 3

Pembahasan

Dengan menggunakan rumus selisih sudut maka Jadi,

Dengan menggunakan rumus selisih sudut $tan space left parenthesis straight A minus straight B right parenthesis equals fraction numerator tan space straight A minus tan space straight B over denominator 1 plus tan space straight A cross times tan space straight B end fraction$ maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 135 degree plus tan space 15 degree end cell equals cell negative 1 plus fraction numerator tan space 45 minus tan space 30 over denominator 1 plus tan space 45 space tan space 30 end fraction end cell row blank equals cell negative 1 plus fraction numerator 1 minus begin display style 1 third end style square root of 3 over denominator 1 plus 1 cross times begin display style 1 third end style square root of 3 end fraction end cell row blank equals cell negative 1 plus fraction numerator 1 minus begin display style fraction numerator square root of 3 over denominator 3 end fraction end style over denominator 1 plus begin display style fraction numerator square root of 3 over denominator 3 end fraction end style end fraction end cell row blank equals cell fraction numerator negative left parenthesis 1 plus begin display style fraction numerator square root of 3 over denominator 3 end fraction end style right parenthesis plus 1 minus begin display style fraction numerator square root of 3 over denominator 3 end fraction end style over denominator 1 plus begin display style fraction numerator square root of 3 over denominator 3 end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator negative 2 square root of 3 over denominator 3 end fraction end style over denominator begin display style fraction numerator 3 plus square root of 3 over denominator 3 end fraction end style end fraction end cell row blank equals cell fraction numerator negative 2 square root of 3 over denominator 3 plus square root of 3 end fraction cross times fraction numerator 3 minus square root of 3 over denominator 3 minus square root of 3 end fraction end cell row blank equals cell fraction numerator negative 6 square root of 3 plus 6 over denominator 9 minus 3 end fraction end cell row blank equals cell fraction numerator negative 6 square root of 3 plus 6 over denominator 6 end fraction end cell row blank equals cell negative square root of 3 plus 1 end cell row blank equals cell 1 minus square root of 3 end cell end table$

Jadi, tan space 135 degree plus tan space 15 degree equals 1 minus square root of 3