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Pertanyaan

Buktikan: b. cos ( a + b ) cos ( a − b ) = cos 2 a − sin 2 b

Buktikan:

b.  

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W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

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terbukti bahwa .

terbukti bahwa cos space open parentheses a plus b close parentheses space cos space open parentheses a minus b close parentheses equals cos squared space a minus sin squared space b.

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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 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 row cell cos space 2 straight A end cell equals cell cos squared space straight A minus sin squared space straight A end cell row blank equals cell 1 minus 2 space sin squared space straight A end cell row blank equals cell 2 space cos squared space straight A minus 1 end cell end table 

Akan dibuktikan cos space open parentheses a plus b close parentheses space cos space open parentheses a minus b close parentheses equals cos squared space a minus sin squared space b. Maka:

 begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell Ruas space kiri end cell equals cell cos space open parentheses a plus b close parentheses space cos space open parentheses a minus b close parentheses end cell row blank equals cell 1 half times 2 times cos space open parentheses a plus b close parentheses space cos space open parentheses a minus b close parentheses end cell row blank equals cell 1 half times open parentheses 2 times cos space open parentheses a plus b close parentheses space cos space open parentheses a minus b close parentheses close parentheses end cell row blank equals cell 1 half open square brackets cos space open parentheses open parentheses a plus b close parentheses plus open parentheses a minus b close parentheses close parentheses plus cos space open parentheses open parentheses a plus b close parentheses minus open parentheses a minus b close parentheses close parentheses close square brackets end cell row blank equals cell 1 half open square brackets cos space open parentheses a up diagonal strike plus b end strike plus a up diagonal strike negative b end strike close parentheses plus cos space open parentheses up diagonal strike a plus b up diagonal strike negative a end strike plus b close parentheses close square brackets end cell row blank equals cell 1 half open parentheses cos space 2 a plus cos space 2 b close parentheses end cell row blank equals cell 1 half open parentheses open parentheses 2 space cos squared space a minus 1 close parentheses plus open parentheses 1 minus 2 space sin squared space b close parentheses close parentheses end cell row blank equals cell 1 half open parentheses 2 space cos squared space a up diagonal strike negative 1 end strike up diagonal strike plus 1 end strike minus 2 space sin squared space b close parentheses end cell row blank equals cell 1 half open parentheses 2 space cos squared space a minus 2 space sin squared space b close parentheses end cell row blank equals cell cos squared space a minus sin squared space b end cell end table end style 

Jadi, terbukti bahwa cos space open parentheses a plus b close parentheses space cos space open parentheses a minus b close parentheses equals cos squared space a minus sin squared space b.

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