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Pertanyaan

Nilai tan space x degree yang memenuhi persamaan: sin open parentheses x plus 30 close parentheses degree equals 2 space cos open parentheses x minus 30 close parentheses degree adalah ...

  1. 4 plus square root of 3 

  2. 4 plus 3 square root of 3 

  3. 4 minus 3 square root of 3 

  4. negative open parentheses 4 plus 3 square root of 3 close parentheses 

  5. 3 minus 4 square root of 3 

H. Firmansyah

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Pembahasan

Akan dicari nilai tan space x degree yang memenuhi persamaan sin open parentheses x plus 30 close parentheses degree equals 2 space cos open parentheses x minus 30 close parentheses degree

Ingat bahwa

tan left parenthesis A plus B right parenthesis equals fraction numerator tan A plus tan B over denominator 1 minus tan A space tan B end fraction tan left parenthesis A minus B right parenthesis equals fraction numerator tan A minus tan B over denominator 1 plus tan A space tan B end fraction sin left parenthesis A plus B right parenthesis equals sin A space cos B plus cos thin space A space sin B cos left parenthesis A minus B right parenthesis equals cos A space cos B plus sin A space sin B 

Diperhatikan

table attributes columnalign right center left columnspacing 0px end attributes row cell sin open parentheses x plus 30 close parentheses degree end cell equals cell 2 space cos open parentheses x minus 30 close parentheses degree end cell row cell sin x degree cos 30 degree plus cos x degree sin 30 degree end cell equals cell 2 open parentheses cos x degree cos 30 degree plus sin x degree sin 30 degree close parentheses end cell row cell sin x degree times 1 half square root of 3 plus cos x degree times 1 half end cell equals cell 2 open parentheses cos x degree times 1 half square root of 3 plus sin x degree times 1 half close parentheses end cell row cell 1 half open parentheses square root of 3 sin x degree plus cos x degree close parentheses end cell equals cell square root of 3 cos x degree plus sin x degree end cell row cell square root of 3 s in x degree plus cos x degree end cell equals cell 2 square root of 3 cos x degree plus 2 sin x degree end cell row cell square root of 3 sin x degree minus 2 sin x degree end cell equals cell 2 square root of 3 cos x degree minus cos x degree end cell row cell open parentheses square root of 3 minus 2 close parentheses sin x degree end cell equals cell open parentheses 2 square root of 3 minus 1 close parentheses cos x degree end cell row cell fraction numerator sin x degree over denominator cos x degree end fraction end cell equals cell fraction numerator 2 square root of 3 minus 1 over denominator square root of 3 minus 2 end fraction end cell row cell tan x degree end cell equals cell fraction numerator 2 square root of 3 minus 1 over denominator square root of 3 minus 2 end fraction cross times fraction numerator square root of 3 plus 2 over denominator square root of 3 plus 2 end fraction end cell row cell tan x degree end cell equals cell fraction numerator 6 plus 3 square root of 3 minus 2 over denominator 3 minus 4 end fraction end cell row cell tan x degree end cell equals cell fraction numerator 4 plus 3 square root of 3 over denominator negative 1 end fraction end cell row cell tan x degree end cell equals cell negative open parentheses 4 plus 3 square root of 3 close parentheses end cell end table 

Dengan demikian, diperoleh nilai tan space x degree adalah negative open parentheses 4 plus 3 square root of 3 close parentheses

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