Jika tan (2x−45∘)=a dan tan (x+15∘)=b, a⋅b∈{−2​, −1, 1, 2​}, maka tan (3x−30∘)⋅tan (x−60∘) sama dengan...

Pertanyaan

Jika tan space open parentheses 2 x minus 45 degree close parentheses equals a dan tan space open parentheses x plus 15 degree close parentheses equals b, a times b not an element of open curly brackets negative square root of 2 comma space minus 1 comma space 1 comma space square root of 2 close curly brackets, maka tan space open parentheses 3 x minus 30 degree close parentheses times tan space open parentheses x minus 60 degree close parentheses sama dengan...

  1. fraction numerator a squared minus b squared over denominator 1 plus a squared b squared end fraction 

  2. fraction numerator a squared plus b squared over denominator 1 minus a squared b squared end fraction 

  3. fraction numerator a squared minus b squared over denominator 1 minus 2 a squared b squared end fraction 

  4. fraction numerator a squared minus b squared over denominator 1 minus a squared b squared end fraction 

  5. fraction numerator a squared plus b squared over denominator 1 plus 2 a squared b squared end fraction 

H. Janatu

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Misalkan table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x minus 45 degree end cell equals cell A space dan space x plus 15 degree equals B end cell end table, sehingga

tan space open parentheses 2 x minus 45 degree close parentheses equals a rightwards arrow tan space A equals a tan space open parentheses x plus 15 degree close parentheses equals b rightwards arrow tan space B equals b

Dengan rumus jumlah dan selisih dua sudut pada tangen,

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space left parenthesis A plus B right parenthesis end cell equals cell fraction numerator tan space A plus tan space B over denominator 1 minus tan space A space tan space B end fraction end cell row cell tan space left parenthesis A minus B right parenthesis end cell equals cell fraction numerator tan space A minus tan space B over denominator 1 plus tan space A space tan space B end fraction end cell end table

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell tan space open parentheses 3 x minus 30 degree close parentheses times tan space open parentheses x minus 60 degree close parentheses end cell row blank equals cell tan space left parenthesis 2 x minus 45 degree plus x plus 15 degree right parenthesis times tan space open parentheses 2 x minus 45 degree minus left parenthesis x plus 15 degree right parenthesis close parentheses end cell row blank equals cell tan space left parenthesis A plus B right parenthesis times tan space left parenthesis A minus B right parenthesis end cell row blank equals cell open parentheses fraction numerator tan space A plus tan space B over denominator 1 minus tan space A space tan space B end fraction close parentheses open parentheses fraction numerator tan space A minus tan space B over denominator 1 plus tan space A space tan space B end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator a plus b over denominator 1 minus a b end fraction close parentheses open parentheses fraction numerator a minus b over denominator 1 plus a b end fraction close parentheses end cell row blank equals cell fraction numerator a squared minus b squared over denominator 1 minus a squared b squared end fraction end cell end table

Jadi, jawaban yang tepat adalah D.

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