Tunjukkanlah setiap bentuk berikut ini. a. tan (4π−A)=cos A+sin Acos A−sin A b. tan (4π+A)=cos A−sin Acos A+sin A c. tan (45+A)∘⋅tan (45−A)∘=1

Pertanyaan

Tunjukkanlah setiap bentuk berikut ini.

a. $tan space open parentheses straight pi over 4 minus A close parentheses equals fraction numerator cos space A minus sin space A over denominator cos space A plus sin space A end fraction$
b. $tan space open parentheses straight pi over 4 plus A close parentheses equals fraction numerator cos space A plus sin space A over denominator cos space A minus sin space A end fraction$
c. $\tan\;\left(45+A\right)^\circ\cdot\tan\;\left(45-A\right)^\circ=1$

H. Janatu

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

pernyataan a, b, dan c terbukti.

Pembahasan

Ingat rumus jumlah dan selisih dua sudut pada tangen :

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

Berdasarkan rumus tersebut, maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight a. space tan space open parentheses straight pi over 4 minus A close parentheses end cell equals cell fraction numerator tan space begin display style straight pi over 4 end style minus tan space A over denominator 1 plus tan space begin display style straight pi over 4 end style tan space A end fraction space space open parentheses tan space straight pi over 4 equals tan space 45 degree equals 1 close parentheses end cell row blank equals cell fraction numerator 1 minus tan space A over denominator 1 plus tan space A end fraction space space space open parentheses tan space A equals fraction numerator sin space A over denominator cos space A end fraction close parentheses end cell row blank equals cell fraction numerator 1 minus fraction numerator sin space A over denominator cos space A end fraction over denominator 1 plus fraction numerator sin space A over denominator cos space A end fraction end fraction cross times fraction numerator cos space A over denominator cos space A end fraction end cell row blank equals cell fraction numerator cos space A minus sin space A over denominator cos space A plus sin space A end fraction space space left parenthesis terbukti right parenthesis end cell row blank blank blank row cell straight b. space tan space open parentheses straight pi over 4 plus straight A close parentheses end cell equals cell fraction numerator tan space straight pi over 4 plus tan space straight A over denominator 1 minus tan space straight pi over 4 tan space straight A end fraction space space open parentheses tan space straight pi over 4 equals tan space 45 degree equals 1 close parentheses end cell row blank equals cell fraction numerator 1 plus tan space straight A over denominator 1 minus tan space straight A end fraction space space space open parentheses tan space straight A equals fraction numerator sin space straight A over denominator cos space straight A end fraction close parentheses end cell row blank equals cell fraction numerator 1 plus fraction numerator sin space straight A over denominator cos space straight A end fraction over denominator 1 minus fraction numerator sin space straight A over denominator cos space straight A end fraction end fraction cross times fraction numerator cos space straight A over denominator cos space straight A end fraction end cell row blank equals cell fraction numerator cos space straight A plus sin space straight A over denominator cos space straight A minus sin space straight A end fraction space space left parenthesis terbukti right parenthesis end cell end table$

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight c. space tan space open parentheses 45 plus A close parentheses degree times tan space open parentheses 45 minus A close parentheses degree end cell equals cell tan space open parentheses straight pi over 4 plus A close parentheses degree times tan space open parentheses straight pi over 4 minus A close parentheses degree end cell row blank equals cell fraction numerator cos space A plus sin space A over denominator cos space A minus sin space A end fraction times fraction numerator cos space A minus sin space A over denominator cos space A plus sin space A end fraction end cell row blank equals cell 1 space left parenthesis terbukti right parenthesis end cell end table end style$

Jadi, pernyataan a, b, dan c terbukti.

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