A+B+C=π​⇒⇒​A+B=π−Ctan (A+B)=tan (π−C)​  Gunakan hubungan tersebut untuk memperoleh relasi: tan A+tan B+tan C=tan A tan B tan C  Lalu, jika tan A=2 dan tan B=34​, buktikan A=C.

Pertanyaan

table row cell straight A plus straight B plus straight C equals straight pi end cell rightwards double arrow cell straight A plus straight B equals straight pi minus straight C end cell row blank rightwards double arrow cell tan space open parentheses straight A plus straight B close parentheses equals tan space open parentheses straight pi minus straight C close parentheses end cell end table 

Gunakan hubungan tersebut untuk memperoleh relasi:

tan space straight A plus tan space straight B plus tan space straight C equals tan space straight A space tan space straight B space tan space straight C 

Lalu, jika tan space straight A equals 2 dan tan space straight B equals 4 over 3, buktikan straight A equals straight C.space 

L. Jannah

Master Teacher

Jawaban terverifikasi

Jawaban

terbukti bahwa straight A equals straight C.

Pembahasan

Sudut Relasi di kuadran II pada Tangen

tan space open parentheses 180 minus alpha close parentheses degree equals negative tan space alpha degree 

Jumlah dan Selisih Dua Sudut pada Tangen

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  

Akan dibuktikan relasi dari tan space straight A plus tan space straight B plus tan space straight C equals tan space straight A space tan space straight B space tan space straight C.

Diketahui tan space open parentheses straight A plus straight B close parentheses equals tan space open parentheses straight pi minus straight C close parentheses dimana straight pi equals 180 degree, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses straight A plus straight B close parentheses end cell equals cell tan space open parentheses straight pi minus straight C close parentheses end cell row cell fraction numerator tan space straight A plus tan space straight B over denominator 1 minus tan space straight A times tan space straight B end fraction end cell equals cell tan space open parentheses 180 degree minus straight C close parentheses end cell row cell fraction numerator tan space straight A plus tan space straight B over denominator 1 minus tan space straight A times tan space straight B end fraction end cell equals cell negative tan space straight C end cell row cell tan space straight A plus tan space straight B end cell equals cell negative tan space straight C space open parentheses 1 minus tan space straight A times tan space straight B close parentheses end cell row cell tan space straight A plus tan space straight B end cell equals cell negative tan space straight C plus tan space straight A times tan space straight B times tan space straight C end cell row cell tan space straight A plus tan space straight B plus tan space straight C end cell equals cell tan space straight A times tan space straight B times tan space straight C end cell end table 

Diketahui pula tan space straight A equals 2 dan tan space straight B equals 4 over 3, akan dibuktikan straight A equals straight C menggunakan relasi:

tan space straight A plus tan space straight B plus tan space straight C equals tan space straight A space tan space straight B space tan space straight C

Bukti:

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space straight A plus tan space straight B plus tan space straight C end cell equals cell tan space straight A space tan space straight B space tan space straight C end cell row cell 2 plus 4 over 3 plus tan space straight C end cell equals cell 2 times 4 over 3 times tan space straight C end cell row cell fraction numerator 2 times 3 over denominator 1 times 3 end fraction plus 4 over 3 plus tan space straight C end cell equals cell 8 over 3 tan space straight C end cell row cell fraction numerator 6 plus 4 over denominator 3 end fraction plus tan space straight C end cell equals cell 8 over 3 tan space straight C end cell row cell 10 over 3 end cell equals cell 8 over 3 tan space straight C minus tan space straight C end cell row cell 10 over 3 end cell equals cell open parentheses 8 over 3 minus 1 close parentheses tan space straight C end cell row cell 10 over 3 end cell equals cell open parentheses 8 over 3 minus 3 over 3 close parentheses tan space straight C end cell row cell fraction numerator 10 over denominator up diagonal strike 3 end fraction end cell equals cell fraction numerator 5 over denominator up diagonal strike 3 end fraction tan space straight C end cell row 10 equals cell 5 space tan space straight C end cell row cell 10 over 5 end cell equals cell tan space straight C end cell row 2 equals cell tan space straight C end cell row cell tan space straight A end cell equals cell tan space straight C end cell end table 

Jadi, terbukti bahwa straight A equals straight C.

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Pertanyaan serupa

Hitunglah tan (A+B) dan tan (A−B) jika : d. tan A=−43​ dan cos B=1312​ dengan A sudut tumpul dan B sudut lancip.

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