Pertanyaan

cot A + cot B tan A + tan B sama dengan ....

$\frac{tan A + tan B}{cot A + cot B}$ sama dengan $....$

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A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

.

$begin mathsize 14px style fraction numerator tan space straight A plus tan space straight B over denominator cot space straight A plus cot space straight B end fraction equals tan space straight A space tan thin space straight B end style$ .

Pembahasan

Rumus tangen dan kotangen adalah Sehingga, Jadi, .

Rumus tangen dan kotangen adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan space straight alpha end cell equals cell fraction numerator sin space straight alpha over denominator cos space straight alpha end fraction end cell row cell cot space straight alpha end cell equals cell fraction numerator 1 over denominator tan space straight alpha end fraction end cell row blank equals cell fraction numerator cos space straight alpha over denominator sin space straight alpha end fraction end cell end table end style$

Sehingga,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator tan space straight A plus tan space straight B over denominator cot space straight A plus cot space straight B end fraction end cell equals cell fraction numerator tan space straight A plus tan space straight B over denominator begin display style fraction numerator 1 over denominator tan space straight A end fraction end style plus begin display style fraction numerator 1 over denominator tan space straight B end fraction end style end fraction end cell row blank equals cell fraction numerator tan space straight A plus tan space straight B over denominator begin display style fraction numerator tan space straight B plus tan space straight A over denominator tan space straight A times tan space straight B end fraction end style end fraction end cell row blank equals cell fraction numerator open parentheses tan space straight A plus tan space straight B close parentheses open parentheses tan space straight A times tan space straight B close parentheses over denominator open parentheses tan space straight A plus tan space straight B close parentheses end fraction end cell row blank equals cell tan space straight A space tan space straight B end cell end table end style$

Jadi, $begin mathsize 14px style fraction numerator tan space straight A plus tan space straight B over denominator cot space straight A plus cot space straight B end fraction equals tan space straight A space tan thin space straight B end style$ .