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Nilai dari sin 10 5 ∘ ⋅ cos 4 5 ∘ + cos 10 5 ∘ ⋅ sin 10 5 ∘ − cos 1 5 ∘ ⋅ sin 4 5 ∘ adalah ....

Nilai dari  adalah ....  

  1. begin mathsize 14px style 1 fourth end style 

  2. begin mathsize 14px style 1 half square root of 3 plus 1 fourth end style 

  3. begin mathsize 14px style negative 1 half square root of 3 plus 1 fourth end style  

  4. begin mathsize 14px style negative 1 half square root of 3 minus 1 fourth end style 

  5. begin mathsize 14px style negative 1 fourth end style 

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

jawaban yang tepat adalah E.

Pembahasan

Ingat kembali identitas-identitas berikut! Akibatnya, diperoleh perhitungan berikut. Lalu, ingat kembali bahwa Akibatnya, didapat perhitungan sebagai berikut. Selanjutnya, perhatikan perhitungan berikut ini! Ingat kembali bahwa Akibatnya, didapat perhitungan sebagai berikut. Kemudian, perhatikan perhitungan berikut! Ingat kembali bahwa Akibatnya, didapat perhitungan berikut. Dengan demikian, diperoleh hasil sebagai berikut. Jadi, jawaban yang tepat adalah E.

Ingat kembali identitas-identitas berikut!

begin mathsize 14px style sin invisible function application A times 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 times 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 

Akibatnya, diperoleh perhitungan berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application 105 degree times cos invisible function application 45 degree end cell equals cell 1 half left parenthesis sin invisible function application open parentheses 105 degree plus 45 degree close parentheses plus sin invisible function application open parentheses 105 degree minus 45 degree close parentheses right parenthesis end cell row blank equals cell 1 half left parenthesis sin invisible function application 150 degree plus sin invisible function application 60 degree right parenthesis end cell row blank equals cell 1 half left parenthesis sin invisible function application open parentheses 180 degree minus 30 degree close parentheses plus sin invisible function application 60 degree right parenthesis end cell end table end style  

Lalu, ingat kembali bahwa

begin mathsize 14px style sin invisible function application left parenthesis 180 degree minus x right parenthesis equals sin invisible function application x end style  

Akibatnya, didapat perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application 105 degree times cos invisible function application 45 degree end cell equals cell 1 half left parenthesis sin invisible function application left parenthesis 180 degree minus 30 degree right parenthesis plus sin invisible function application 60 degree right parenthesis end cell row blank equals cell 1 half left parenthesis sin invisible function application 30 degree plus sin invisible function application 60 degree right parenthesis end cell row blank equals cell 1 half open parentheses 1 half plus 1 half square root of 3 close parentheses end cell row blank equals cell 1 fourth plus 1 fourth square root of 3 end cell row blank blank blank end table end style   

Selanjutnya, perhatikan perhitungan berikut ini!

begin mathsize 14px style cos invisible function application 105 degree times sin invisible function application 105 degree equals 1 half left parenthesis sin invisible function application left parenthesis 105 degree plus 105 degree right parenthesis minus sin invisible function application left parenthesis 105 degree minus 105 degree right parenthesis right parenthesis equals 1 half left parenthesis sin invisible function application 210 degree minus sin invisible function application 0 degree right parenthesis equals 1 half left parenthesis sin invisible function application left parenthesis 180 degree plus 30 degree right parenthesis minus sin invisible function application 0 degree right parenthesis end style 

Ingat kembali bahwa

begin mathsize 14px style sin invisible function application left parenthesis 180 degree plus x right parenthesis equals negative sin invisible function application x end style  

Akibatnya, didapat perhitungan sebagai berikut.

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

Kemudian, perhatikan perhitungan berikut!

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell cos invisible function application 15 degree times sin invisible function application 45 degree end cell row blank equals cell 1 half left parenthesis sin invisible function application open parentheses 15 degree plus 45 degree close parentheses minus sin invisible function application open parentheses 15 degree minus 45 degree close parentheses right parenthesis end cell row blank equals cell 1 half left parenthesis sin invisible function application 60 degree minus sin invisible function application open parentheses negative 30 degree close parentheses right parenthesis end cell end table 

Ingat kembali bahwa

begin mathsize 14px style sin left parenthesis negative x right parenthesis equals negative sin space x end style 

Akibatnya, didapat perhitungan berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell cos invisible function application 15 degree times sin invisible function application 45 degree end cell equals cell 1 half left parenthesis sin invisible function application 60 degree minus sin invisible function application open parentheses negative 30 degree close parentheses right parenthesis end cell row blank equals cell 1 half left parenthesis sin invisible function application 60 degree minus open parentheses negative sin invisible function application 30 degree close parentheses right parenthesis end cell row blank equals cell 1 half left parenthesis sin invisible function application 60 degree plus sin invisible function application 30 degree right parenthesis end cell row blank equals cell 1 half open parentheses 1 half square root of 3 plus 1 half close parentheses end cell row blank equals cell 1 fourth square root of 3 plus 1 fourth end cell end table  

Dengan demikian, diperoleh hasil sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank invisible function application end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 105 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table times table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank invisible function application end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 45 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank invisible function application end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 105 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell times sin end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank invisible function application end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 105 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank invisible function application end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 15 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell degree times end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank invisible function application end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 45 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 1 fourth plus 1 fourth square root of 3 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses negative 1 fourth close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 1 fourth square root of 3 plus 1 fourth close parentheses end cell end table equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 fourth end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 fourth end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 fourth end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 fourth end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 fourth end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 fourth end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table   

Jadi, jawaban yang tepat adalah E.

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