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 space open parentheses 45 plus A close parentheses degree times tan space open parentheses 45 minus A close parentheses degree equals 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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