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Buktikan identitas berikut. c. 2 cos ( θ + 4 π ​ ) ⋅ cos ( 4 3 π ​ − θ ) + 1 = sin 2 θ

Buktikan identitas berikut.

c.  

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Jawaban terverifikasi

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terbukti bahwa .

terbukti bahwa 2 space cos space open parentheses straight theta plus straight pi over 4 close parentheses times cos space open parentheses fraction numerator 3 straight pi over denominator 4 end fraction minus straight theta close parentheses plus 1 equals sin space 2 straight theta.

Pembahasan

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

Ingat kembali:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 space cos space straight alpha space cos space straight beta end cell equals cell 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 row cell cos space open parentheses 90 degree minus straight A close parentheses end cell equals cell sin space straight A end cell end table 

Akan dibuktikan 2 space cos space open parentheses straight theta plus straight pi over 4 close parentheses times cos space open parentheses fraction numerator 3 straight pi over denominator 4 end fraction minus straight theta close parentheses plus 1 equals sin 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 2 space cos space open parentheses straight theta plus straight pi over 4 close parentheses times cos space open parentheses fraction numerator 3 straight pi over denominator 4 end fraction minus straight theta close parentheses plus 1 end cell row blank equals cell open square brackets cos space open parentheses open parentheses straight theta plus straight pi over 4 close parentheses plus open parentheses fraction numerator 3 straight pi over denominator 4 end fraction minus straight theta close parentheses close parentheses plus cos space open parentheses open parentheses straight theta plus straight pi over 4 close parentheses minus open parentheses fraction numerator 3 straight pi over denominator 4 end fraction minus straight theta close parentheses close parentheses close square brackets plus 1 end cell row blank equals cell open square brackets cos space open parentheses up diagonal strike straight theta plus straight pi over 4 plus fraction numerator 3 straight pi over denominator 4 end fraction up diagonal strike negative straight theta end strike close parentheses plus cos space open parentheses straight theta plus straight pi over 4 minus fraction numerator 3 straight pi over denominator 4 end fraction plus straight theta close parentheses close square brackets plus 1 end cell row blank equals cell open square brackets cos space open parentheses 4 over 4 straight pi close parentheses plus cos space open parentheses 2 straight theta minus 2 over 4 straight pi close parentheses close square brackets plus 1 end cell row blank equals cell open parentheses cos space 180 degree plus cos space open parentheses 2 straight theta minus 90 degree close parentheses close parentheses plus 1 end cell row blank equals cell open parentheses negative 1 plus sin space 2 straight theta close parentheses plus 1 end cell row blank equals cell up diagonal strike negative 1 end strike plus sin space 2 straight theta up diagonal strike plus 1 end strike end cell row blank equals cell sin space 2 straight theta end cell end table end style 

Jadi, terbukti bahwa 2 space cos space open parentheses straight theta plus straight pi over 4 close parentheses times cos space open parentheses fraction numerator 3 straight pi over denominator 4 end fraction minus straight theta close parentheses plus 1 equals sin space 2 straight theta.

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