Pertanyaan

Tunjukkan bahwa: cos 4 5 ∘ + sin 4 5 ∘ tan 22 , 5 ∘ = 1

Tunjukkan bahwa:

$cos 4 5^{\circ} + sin 4 5^{\circ} tan 22, 5^{\circ} = 1$

T. Prita

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa cos space 45 degree plus sin space 45 degree space tan space 22 comma 5 degree equals 1

Pembahasan

Ingatlah rumussudut paruh pada tangen yaitu: Sehingga diperoleh: dengan Kemudian, diperoleh penyelesaiannya yaitu: Dengan demikian, terbukti bahwa .

Ingatlah rumus sudut paruh pada tangen yaitu:

Sehingga diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 22 comma 5 degree end cell equals cell tan space open parentheses alpha over 2 close parentheses end cell row alpha equals cell tan space 22 comma 5 degree times 2 end cell row alpha equals cell 45 degree end cell end table

dengan

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses alpha over 2 close parentheses end cell equals cell fraction numerator 1 minus cos space alpha over denominator sin space alpha end fraction end cell row cell tan space open parentheses fraction numerator 45 degree over denominator 2 end fraction close parentheses end cell equals cell fraction numerator 1 minus cos space 45 degree over denominator sin space 45 degree end fraction end cell end table$

Kemudian, diperoleh penyelesaiannya yaitu:

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 45 degree plus sin space 45 degree space tan space 22 comma 5 degree end cell equals 1 row cell 1 half square root of 2 plus 1 half square root of 2 times tan space 22 comma 5 degree end cell equals 1 row cell 1 half square root of 2 plus fraction numerator square root of 2 times tan space 22 comma 5 degree over denominator 2 end fraction end cell equals 1 row cell 1 half square root of 2 plus fraction numerator square root of 2 times begin display style fraction numerator 1 minus cos space 45 degree over denominator sin space 45 degree end fraction end style over denominator 2 end fraction end cell equals 1 row cell 1 half square root of 2 plus fraction numerator square root of 2 times begin display style fraction numerator 1 minus begin display style 1 half end style square root of 2 over denominator begin display style 1 half end style square root of 2 end fraction end style over denominator 2 end fraction end cell equals 1 row cell 1 half square root of 2 plus fraction numerator square root of 2 times begin display style fraction numerator begin display style fraction numerator 2 over denominator down diagonal strike 2 end fraction end style minus begin display style fraction numerator 1 over denominator down diagonal strike 2 end fraction end style square root of 2 over denominator begin display style fraction numerator 1 over denominator down diagonal strike 2 end fraction end style square root of 2 end fraction end style over denominator 2 end fraction end cell equals 1 row cell 1 half square root of 2 plus fraction numerator down diagonal strike square root of 2 end strike times begin display style fraction numerator begin display style 2 minus square root of 2 end style over denominator begin display style down diagonal strike square root of 2 end strike end style end fraction end style over denominator 2 end fraction end cell equals 1 row cell 1 half square root of 2 plus fraction numerator begin display style 2 minus square root of 2 end style over denominator 2 end fraction end cell equals 1 row cell 1 half square root of 2 plus 1 minus 1 half square root of 2 end cell equals 1 row 1 equals 1 end table$

Dengan demikian, terbukti bahwa cos space 45 degree plus sin space 45 degree space tan space 22 comma 5 degree equals 1 .