Pertanyaan

[UN 2006 IPA] Nilai tan 75 o adalah …

[UN 2006 IPA]

Nilai tan 75^o adalah …

A. Nadhira

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Ingat rumus sehingga

Ingat rumus $tan space left parenthesis a plus b right parenthesis equals fraction numerator tan space a plus tan space b over denominator 1 minus tan space a space tan space b end fraction comma$ sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 75 to the power of o space end cell equals cell space tan left parenthesis 45 to the power of o plus 30 to the power of o right parenthesis end cell row blank equals cell fraction numerator tan space 45 to the power of o plus tan space 30 to the power of o over denominator 1 minus tan space 45 to the power of o. space tan space 30 to the power of o end fraction end cell row blank equals cell fraction numerator 1 plus begin display style 1 third end style square root of 3 over denominator 1 minus 1. begin display style 1 third end style square root of 3 end fraction end cell row blank equals cell fraction numerator 1 plus begin display style 1 third end style square root of 3 over denominator 1 minus begin display style 1 third end style square root of 3 end fraction cross times fraction numerator 1 plus begin display style 1 third end style square root of 3 over denominator 1 plus begin display style 1 third end style square root of 3 end fraction end cell row blank equals cell fraction numerator begin display style 1 plus 1 third square root of 3 plus 1 third square root of 3 plus 1 third end style over denominator begin display style 1 minus 1 third end style end fraction end cell row blank equals cell fraction numerator begin display style 4 over 3 end style plus 2 over 3 square root of 3 over denominator begin display style 2 over 3 end style end fraction end cell row blank equals cell open parentheses 4 over 3 plus 2 over 3 square root of 3 close parentheses cross times 3 over 2 end cell row blank equals cell 12 over 6 plus 6 over 6 square root of 3 end cell row blank equals cell 2 plus square root of 3 end cell end table$