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Jika tan α tan β=1, maka tan (α+β)tan (α−β)​ sama dengan ...

Pertanyaan

Jika tan space alpha space tan space beta equals 1, maka fraction numerator tan space open parentheses alpha minus beta close parentheses over denominator tan space open parentheses alpha plus beta close parentheses end fraction sama dengan ...

  1. negative 2

  2. negative 1

  3. 0

  4. 1

  5. 2

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Rumus tangen untuk jumlah dan selisih dua sudut, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses alpha plus beta close parentheses end cell equals cell fraction numerator tan space alpha plus tan space beta over denominator 1 minus tan space alpha times tan space beta end fraction end cell row cell tan space open parentheses alpha minus beta close parentheses end cell equals cell fraction numerator tan space alpha minus tan space beta over denominator 1 plus tan space alpha times tan space beta end fraction end cell end table

Diketahui tan space alpha space tan space beta equals 1, maka diperoleh nilai fraction numerator tan space open parentheses alpha minus beta close parentheses over denominator tan space open parentheses alpha plus beta close parentheses end fraction yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator tan space open parentheses alpha minus beta close parentheses over denominator tan space open parentheses alpha plus beta close parentheses end fraction end cell equals cell fraction numerator begin display style fraction numerator tan space alpha minus tan space beta over denominator 1 plus tan space alpha times tan space beta end fraction end style over denominator begin display style fraction numerator tan space alpha plus tan space beta over denominator 1 minus tan space alpha times tan space beta end fraction end style end fraction end cell row blank equals cell fraction numerator tan space alpha minus tan space beta over denominator 1 plus tan space alpha times tan space beta end fraction divided by fraction numerator tan space alpha plus tan space beta over denominator 1 minus tan space alpha times tan space beta end fraction end cell row blank equals cell fraction numerator open parentheses tan space alpha minus tan space beta close parentheses over denominator open parentheses 1 plus tan space alpha times tan space beta close parentheses end fraction times fraction numerator open parentheses 1 minus tan space alpha times tan space beta close parentheses over denominator open parentheses tan space alpha plus tan space beta close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses tan space alpha minus tan space beta close parentheses over denominator open parentheses 1 plus 1 close parentheses end fraction times fraction numerator open parentheses 1 minus 1 close parentheses over denominator open parentheses tan space alpha plus tan space beta close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses tan space alpha minus tan space beta close parentheses over denominator 2 end fraction times fraction numerator 0 over denominator open parentheses tan space alpha plus tan space beta close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses tan space alpha minus tan space beta close parentheses over denominator 2 end fraction times 0 end cell row blank equals 0 end table


Jadi, fraction numerator tan space open parentheses alpha minus beta close parentheses over denominator tan space open parentheses alpha plus beta close parentheses end fraction sama dengan 0.

Oleh karena itu, jawaban yang benar adalah C.

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