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Pertanyaan

Buktikan: a. 2 sin ( 4 1 ​ π + α ) sin ( 4 3 ​ π + α ) = cos 2 α

Buktikan:

a.  

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S. Nur

Master Teacher

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terbukti bahwa .

terbukti bahwa 2 space sin space open parentheses 1 fourth straight pi plus straight alpha close parentheses space sin space open parentheses 3 over 4 straight pi plus straight alpha close parentheses equals cos space 2 straight alpha .

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Pembahasan

Ingat kembali: Akan dibuktikan . Maka: Jadi, terbukti bahwa .

Ingat kembali:

2 space sin space straight alpha space sin space straight beta equals negative cos space open parentheses straight alpha plus straight beta close parentheses plus cos space open parentheses straight alpha minus straight beta close parentheses cos space open parentheses 180 degree plus straight A close parentheses equals negative cos space straight A 

Akan dibuktikan 2 space sin space open parentheses 1 fourth straight pi plus straight alpha close parentheses space sin space open parentheses 3 over 4 straight pi plus straight alpha close parentheses equals cos space 2 straight alpha . Maka:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell Ruas space kiri end cell equals cell 2 space sin space open parentheses 1 fourth straight pi plus straight alpha close parentheses space sin space open parentheses 3 over 4 straight pi plus straight alpha close parentheses end cell row blank equals cell negative cos space open parentheses open parentheses 1 fourth straight pi plus straight alpha close parentheses plus open parentheses 3 over 4 straight pi plus straight alpha close parentheses close parentheses plus cos space open parentheses open parentheses 1 fourth straight pi plus straight alpha close parentheses minus open parentheses 3 over 4 straight pi plus straight alpha close parentheses close parentheses end cell row blank equals cell negative cos space open parentheses 1 fourth straight pi plus straight alpha plus 3 over 4 straight pi plus straight alpha close parentheses plus cos space open parentheses 1 fourth straight pi up diagonal strike plus straight alpha end strike minus 3 over 4 straight pi up diagonal strike negative straight alpha end strike close parentheses end cell row blank equals cell negative cos space open parentheses 4 over 4 straight pi plus 2 straight alpha close parentheses plus cos space open parentheses negative 2 over 4 straight pi close parentheses end cell row blank equals cell negative cos space open parentheses 180 degree plus 2 straight a close parentheses minus cos space 90 degree end cell row blank equals cell negative open parentheses negative cos space 2 straight alpha close parentheses minus 0 end cell row blank equals cell cos space 2 straight alpha end cell end table end style  

Jadi, terbukti bahwa 2 space sin space open parentheses 1 fourth straight pi plus straight alpha close parentheses space sin space open parentheses 3 over 4 straight pi plus straight alpha close parentheses equals cos space 2 straight alpha .

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