Jika cos (A−B)=53​ dan tan A tan B=2, hitunglah: c. cos(A+B)

Pertanyaan

Jika cos space open parentheses A minus B close parentheses equals 3 over 5 dan tan space A space tan space B equals 2, hitunglah:

c. cos open parentheses A plus B close parentheses 

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

diperoleh cos open parentheses A plus B close parentheses equals negative 1 fifth.

Pembahasan

Diketahui cos open parentheses A minus B close parentheses equals 3 over 5 dan tan open parentheses A close parentheses tan open parentheses B close parentheses equals 2. Akan dicari cos open parentheses A plus B close parentheses

Ingat bahwa

cos left parenthesis A minus B right parenthesis equals cos left parenthesis A right parenthesis cos left parenthesis B right parenthesis plus sin left parenthesis A right parenthesis sin left parenthesis B right parenthesis cos left parenthesis A plus B right parenthesis equals cos left parenthesis A right parenthesis cos left parenthesis B right parenthesis minus sin left parenthesis A right parenthesis sin left parenthesis B right parenthesis 

Diperhatikan

tan open parentheses A close parentheses times tan open parentheses B close parentheses equals 2 rightwards double arrow fraction numerator sin left parenthesis A right parenthesis over denominator cos left parenthesis A right parenthesis end fraction times fraction numerator sin left parenthesis B right parenthesis over denominator cos left parenthesis B right parenthesis end fraction equals 2 rightwards double arrow sin left parenthesis A right parenthesis times sin left parenthesis B right parenthesis equals 2 space cos left parenthesis A right parenthesis times cos left parenthesis B right parenthesis 

dan

 tan open parentheses A close parentheses times tan open parentheses B close parentheses equals 2 rightwards double arrow fraction numerator sin left parenthesis A right parenthesis over denominator cos left parenthesis A right parenthesis end fraction times fraction numerator sin left parenthesis B right parenthesis over denominator cos left parenthesis B right parenthesis end fraction equals 2 rightwards double arrow fraction numerator sin left parenthesis A right parenthesis times sin left parenthesis B right parenthesis over denominator 2 end fraction equals cos left parenthesis A right parenthesis times cos left parenthesis B right parenthesis 

Diperoleh perhitungan

table attributes columnalign right center left columnspacing 0px end attributes row cell cos left parenthesis A minus B right parenthesis end cell equals cell 3 over 5 end cell row cell cos left parenthesis A right parenthesis cos left parenthesis B right parenthesis plus sin left parenthesis A right parenthesis sin left parenthesis B right parenthesis end cell equals cell 3 over 5 end cell row cell cos left parenthesis A right parenthesis cos left parenthesis B right parenthesis plus 2 cos left parenthesis A right parenthesis cos left parenthesis B right parenthesis end cell equals cell 3 over 5 end cell row cell 3 cos left parenthesis A right parenthesis cos left parenthesis B right parenthesis end cell equals cell 3 over 5 end cell row cell cos left parenthesis A right parenthesis cos left parenthesis B right parenthesis end cell equals cell 3 over 5 times 1 third end cell row cell cos left parenthesis A right parenthesis cos left parenthesis B right parenthesis end cell equals cell 1 fifth end cell end table 

dan 

table attributes columnalign right center left columnspacing 0px end attributes row cell cos left parenthesis A minus B right parenthesis end cell equals cell 3 over 5 end cell row cell cos left parenthesis A right parenthesis cos left parenthesis B right parenthesis plus sin left parenthesis A right parenthesis sin left parenthesis B right parenthesis end cell equals cell 3 over 5 end cell row cell fraction numerator sin left parenthesis A right parenthesis sin left parenthesis B right parenthesis over denominator 2 end fraction plus sin left parenthesis A right parenthesis sin left parenthesis B right parenthesis end cell equals cell 3 over 5 end cell row cell 3 over 2 sin left parenthesis A right parenthesis sin left parenthesis B right parenthesis end cell equals cell 3 over 5 end cell row cell sin left parenthesis A right parenthesis sin left parenthesis B right parenthesis end cell equals cell 3 over 5 times 2 over 3 end cell row cell sin left parenthesis A right parenthesis sin left parenthesis B right parenthesis end cell equals cell 2 over 5 end cell end table

Lebih lanjut, diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell cos left parenthesis A plus B right parenthesis end cell equals cell cos left parenthesis A right parenthesis cos left parenthesis B right parenthesis minus sin left parenthesis A right parenthesis sin left parenthesis B right parenthesis end cell row blank equals cell 1 fifth minus 2 over 5 end cell row blank equals cell negative 1 fifth end cell end table 

Dengan demikian, diperoleh cos open parentheses A plus B close parentheses equals negative 1 fifth.

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Jika cos (A−B)=53​ dan tan A tan B=2, hitunglah: b. cos A cos B

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Jawaban terverifikasi

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