Pertanyaan

Nilai dari cot 112 , 5 ∘ tan 22 , 5 ∘ adalah ....

Nilai dari $cot 112, 5^{\circ} tan 22, 5^{\circ}$ adalah ....

$begin mathsize 14px style fraction numerator square root of 3 minus 2 over denominator 2 plus square root of 2 end fraction end style$
$begin mathsize 14px style fraction numerator square root of 3 plus 2 over denominator 2 plus square root of 2 end fraction end style$
$begin mathsize 14px style fraction numerator square root of 2 minus 2 over denominator 2 plus square root of 2 end fraction end style$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Perhatikan bahwa Kemudian, dengan menggunakan rumus sudut paruh pada ,perhatikan bahwa Perhatikan bahwa sudut berada di kuadran II sehingga akanbernilai negatif. Akibatnya, diambil . Selanjutnya, dengan menggunakan sudut paruh pada , didapat perhitungan sebagai berikut. Perhatikan bahwa sudut berada di kuadran I sehingga akanbernilai positif. Akibatnya, diperoleh . Dengan demikian, didapat hasil sebagai berikut. Jadi, jawaban yang tepat adalah E.

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cot invisible function application 112 , 5 degree times tan invisible function application 22 , 5 degree end cell equals cell cot invisible function application 1 half left parenthesis 225 degree right parenthesis times tan invisible function application 1 half left parenthesis 45 degree right parenthesis end cell row blank equals cell fraction numerator 1 over denominator tan invisible function application 1 half left parenthesis 225 degree right parenthesis end fraction times tan invisible function application 1 half left parenthesis 45 degree right parenthesis end cell end table end style$

Kemudian, dengan menggunakan rumus sudut paruh pada tan 1 half open parentheses 225 degree close parentheses , perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan invisible function application 1 half open parentheses 225 degree close parentheses end cell equals cell plus-or-minus square root of fraction numerator 1 minus cos invisible function application 225 degree over denominator 1 plus cos invisible function application 225 degree end fraction end root end cell row blank equals cell plus-or-minus square root of fraction numerator 1 minus cos invisible function application open parentheses 180 degree plus 45 degree close parentheses over denominator 1 plus cos invisible function application open parentheses 180 degree plus 45 degree close parentheses end fraction end root end cell row blank equals cell plus-or-minus square root of fraction numerator 1 minus open parentheses negative cos invisible function application 45 degree close parentheses over denominator 1 plus open parentheses negative cos invisible function application 45 degree close parentheses end fraction end root end cell row blank equals cell plus-or-minus square root of fraction numerator 1 plus cos invisible function application 45 degree over denominator 1 minus cos invisible function application 45 degree end fraction end root end cell row blank equals cell plus-or-minus square root of fraction numerator 1 plus 1 half square root of 2 over denominator 1 minus 1 half square root of 2 end fraction end root end cell row blank equals cell plus-or-minus square root of fraction numerator 1 plus 1 half square root of 2 over denominator 1 minus 1 half square root of 2 end fraction times 2 over 2 end root end cell row blank equals cell plus-or-minus square root of fraction numerator 2 plus square root of 2 over denominator 2 minus square root of 2 end fraction end root end cell end table end style$

Perhatikan bahwa sudut 1 half open parentheses 225 degree close parentheses equals 112 comma 5 degree berada di kuadran II sehingga tan invisible function application 112 comma 5 degree akan bernilai negatif.

Akibatnya, diambil $begin mathsize 14px style tan invisible function application 112 , 5 degree equals negative square root of fraction numerator 2 plus square root of 2 over denominator 2 minus square root of 2 end fraction end root end style$ .

Selanjutnya, dengan menggunakan sudut paruh pada tan 1 half open parentheses 45 degree close parentheses , didapat perhitungan sebagai berikut.

Perhatikan bahwa sudut 1 half open parentheses 45 degree close parentheses equals 22 comma 5 degree berada di kuadran I sehingga tan invisible function application 22 comma 5 degree akan bernilai positif.

Akibatnya, diperoleh $begin mathsize 14px style tan invisible function application 22 , 5 degree equals square root of fraction numerator 2 minus square root of 2 over denominator 2 plus square root of 2 end fraction end root end style$ .

Dengan demikian, didapat hasil sebagai berikut.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cot invisible function application 112 , 5 degree tan invisible function application 22 , 5 degree end cell equals cell fraction numerator 1 over denominator tan invisible function application 1 half open parentheses 225 degree close parentheses end fraction times tan invisible function application 1 half open parentheses 45 degree close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative square root of fraction numerator 2 plus square root of 2 over denominator 2 minus square root of 2 end fraction end root end fraction times square root of fraction numerator 2 minus square root of 2 over denominator 2 plus square root of 2 end fraction end root end cell row blank equals cell negative square root of fraction numerator 2 minus square root of 2 over denominator 2 plus square root of 2 end fraction end root times square root of fraction numerator 2 minus square root of 2 over denominator 2 plus square root of 2 end fraction end root end cell row blank equals cell negative fraction numerator 2 minus square root of 2 over denominator 2 plus square root of 2 end fraction end cell row blank equals cell fraction numerator square root of 2 minus 2 over denominator 2 plus square root of 2 end fraction end cell end table end style$

Jadi, jawaban yang tepat adalah E.