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Pertanyaan

cos 75° sin 75° + sin 15° cos 105° + cos 105° sin 75° = ....

cos75° sin75° + sin15° cos105° + cos105° sin75° =  ....

  1. begin mathsize 12px style 1 half square root of 3 minus 1 fourth end style 

  2. begin mathsize 12px style 1 half square root of 3 plus 1 fourth end style 

  3. begin mathsize 12px style 1 fourth square root of 3 minus 1 half end style 

  4. begin mathsize 12px style 1 fourth square root of 3 plus 1 half end style 

  5. begin mathsize 12px style 1 half minus 1 fourth square root of 3 end style 

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R. Mahmudah

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Jawaban terverifikasi

Pembahasan

Ingat bahwa Sehingga Ingat bahwa sin( 180° - x) = sin x Sehingga Selanjutnya Ingat bahwa Sehingga Kemudian Maka Jadi, jawaban yang tepat adalah C.

Ingat bahwa

begin mathsize 12px style sin invisible function application A cos invisible function application B equals 1 half open parentheses sin invisible function application open parentheses A plus B close parentheses plus sin invisible function application open parentheses A minus B close parentheses close parentheses cos invisible function application A sin invisible function application B equals 1 half open parentheses sin invisible function application open parentheses A plus B close parentheses minus sin invisible function application open parentheses A minus B close parentheses close parentheses end style 

Sehingga

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos invisible function application 75 degree sin invisible function application 75 degree end cell equals cell 1 half open parentheses sin invisible function application open parentheses 75 degree plus 75 degree close parentheses minus sin invisible function application open parentheses 75 degree minus 75 degree close parentheses close parentheses end cell row blank equals cell 1 half open parentheses sin invisible function application 150 degree minus sin invisible function application 0 degree close parentheses end cell row blank equals cell 1 half open parentheses sin invisible function application open parentheses 180 degree minus 30 degree close parentheses minus sin invisible function application 0 degree close parentheses space end cell end table end style 

Ingat bahwa

sin(180° - x) = sin x
Sehingga

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos invisible function application 75 degree sin invisible function application 75 degree end cell equals cell 1 half open parentheses sin invisible function application open parentheses 180 degree minus 30 degree close parentheses minus sin invisible function application 0 degree close parentheses end cell row blank equals cell 1 half open parentheses sin invisible function application 30 degree minus sin invisible function application 0 degree close parentheses end cell row blank equals cell 1 half open parentheses 1 half minus 0 close parentheses end cell row blank equals cell 1 fourth end cell end table end style 

Selanjutnya

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application 15 degree cos invisible function application 105 degree end cell equals cell 1 half open parentheses sin invisible function application open parentheses 15 degree plus 105 degree close parentheses plus sin invisible function application open parentheses 15 degree minus 105 degree close parentheses close parentheses end cell row blank equals cell 1 half open parentheses sin invisible function application 120 degree plus sin invisible function application open parentheses negative 90 degree close parentheses close parentheses end cell row blank equals cell 1 half open parentheses sin invisible function application open parentheses 180 degree minus 60 degree close parentheses plus sin invisible function application open parentheses negative 90 degree close parentheses close parentheses end cell end table end style 

Ingat bahwa

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application open parentheses 180 degree minus x close parentheses end cell equals cell sin invisible function application x end cell row cell sin invisible function application open parentheses negative x close parentheses end cell equals cell negative sin invisible function application x end cell end table end style 

Sehingga

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application 15 degree cos invisible function application 105 degree end cell equals cell 1 half open parentheses sin invisible function application open parentheses 180 degree minus 60 degree close parentheses plus sin invisible function application open parentheses negative 90 degree close parentheses close parentheses end cell row blank equals cell 1 half open parentheses sin invisible function application 60 degree minus sin invisible function application 90 degree close parentheses end cell row blank equals cell 1 half open parentheses 1 half square root of 3 minus 1 close parentheses end cell row blank equals cell 1 fourth square root of 3 minus 1 half end cell row blank blank blank end table end style 

Kemudian

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos invisible function application 105 degree sin invisible function application 75 degree end cell equals cell 1 half open parentheses sin invisible function application open parentheses 105 degree plus 75 degree close parentheses minus sin invisible function application open parentheses 105 degree minus 75 degree close parentheses close parentheses end cell row blank equals cell 1 half open parentheses sin invisible function application 180 degree minus sin invisible function application 30 degree close parentheses end cell row blank equals cell 1 half open parentheses 0 minus 1 half close parentheses end cell row blank equals cell negative 1 fourth end cell end table end style 

Maka

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell cos invisible function application 75 degree sin invisible function application 75 degree plus sin invisible function application 15 degree cos invisible function application 105 degree plus cos invisible function application 105 degree sin invisible function application 75 degree end cell row blank equals cell 1 fourth plus open parentheses 1 fourth square root of 3 minus 1 half close parentheses plus open parentheses negative 1 fourth close parentheses end cell row blank equals cell 1 fourth plus 1 fourth square root of 3 minus 1 half minus 1 fourth end cell row blank equals cell 1 fourth square root of 3 minus 1 half end cell row blank blank blank end table end style 

Jadi, jawaban yang tepat adalah C.

 

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