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Buktikan identitas berikut. d. sin ( 4 π ​ + θ ) ⋅ sin ( 4 π ​ − θ ) = 2 1 ​ cos 2 θ

Buktikan identitas berikut.

d.  

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W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

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terbukti bahwa .

terbukti bahwa sin space open parentheses straight pi over 4 plus straight theta close parentheses times sin space open parentheses straight pi over 4 minus straight theta close parentheses equals 1 half space cos space 2 straight theta.

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

Ingat kembali:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 space sin space straight alpha space sin space straight beta end cell equals cell negative cos space open parentheses straight alpha plus straight beta close parentheses plus cos space open parentheses straight alpha minus straight beta close parentheses end cell end table 

Akan dibuktikan sin space open parentheses straight pi over 4 plus straight theta close parentheses times sin space open parentheses straight pi over 4 minus straight theta close parentheses equals 1 half space cos space 2 straight theta. Maka:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell Ruas space kiri end cell equals cell sin space open parentheses straight pi over 4 plus straight theta close parentheses times sin space open parentheses straight pi over 4 minus straight theta close parentheses end cell row blank equals cell 1 half times 2 times sin space open parentheses straight pi over 4 plus straight theta close parentheses times sin space open parentheses straight pi over 4 minus straight theta close parentheses end cell row blank equals cell 1 half times open parentheses 2 times sin space open parentheses straight pi over 4 plus straight theta close parentheses times sin space open parentheses straight pi over 4 minus straight theta close parentheses close parentheses end cell row blank equals cell 1 half open square brackets negative cos space open parentheses open parentheses straight pi over 4 plus straight theta close parentheses plus open parentheses straight pi over 4 minus straight theta close parentheses close parentheses plus cos space open parentheses open parentheses straight pi over 4 plus straight theta close parentheses minus open parentheses straight pi over 4 minus straight theta close parentheses close parentheses close square brackets end cell row blank equals cell 1 half open square brackets negative cos space open parentheses straight pi over 4 up diagonal strike plus straight theta end strike plus straight pi over 4 up diagonal strike negative straight theta end strike close parentheses plus cos space open parentheses up diagonal strike straight pi over 4 end strike plus straight theta up diagonal strike negative straight pi over 4 end strike plus straight theta close parentheses close square brackets end cell row blank equals cell 1 half open square brackets negative cos space open parentheses fraction numerator 2 straight pi over denominator 4 end fraction close parentheses plus cos space 2 straight theta close square brackets end cell row blank equals cell 1 half open parentheses negative cos space 90 degree plus cos space 2 straight theta close parentheses end cell row blank equals cell 1 half open parentheses 0 plus cos space 2 straight theta close parentheses end cell row blank equals cell 1 half open parentheses cos space 2 straight theta close parentheses end cell row blank equals cell 1 half space cos space 2 straight theta end cell end table end style 

Jadi, terbukti bahwa sin space open parentheses straight pi over 4 plus straight theta close parentheses times sin space open parentheses straight pi over 4 minus straight theta close parentheses equals 1 half space cos space 2 straight theta.

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