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Buktikan identitas berikut. b. 2 cos θ ⋅ sin 3 θ = sin 2 θ ( 2 cos 2 θ + 1 )

Buktikan identitas berikut.

b.  

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W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

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terbukti bahwa .

terbukti bahwa 2 space cos space straight theta times sin space 3 straight theta equals sin space 2 straight theta space open parentheses 2 space cos space 2 straight theta plus 1 close parentheses.

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

Ingat kembali:

2 space cos space straight alpha space sin space straight beta equals sin space open parentheses straight alpha plus straight beta close parentheses minus sin space open parentheses straight alpha minus straight beta close parentheses sin space 2 straight A equals 2 times sin space straight A times cos space straight A 

Akan dibuktikan 2 space cos space straight theta times sin space 3 straight theta equals sin space 2 straight theta space open parentheses 2 space cos space 2 straight theta plus 1 close parentheses. Maka:

  table attributes columnalign right center left columnspacing 0px end attributes row cell Ruas space kiri end cell equals cell 2 space cos space straight theta times sin space 3 straight theta end cell row blank equals cell sin space open parentheses straight theta plus 3 straight theta close parentheses minus sin space open parentheses straight theta minus 3 straight theta close parentheses end cell row blank equals cell sin space 4 straight theta minus sin space open parentheses negative 2 straight theta close parentheses end cell row blank equals cell sin space 4 straight theta plus sin space 2 straight theta end cell row blank equals cell 2 times sin space 2 straight theta times cos space 2 straight theta plus sin space 2 straight theta end cell row blank equals cell sin space 2 straight theta space open parentheses 2 space cos space 2 straight theta plus 1 close parentheses end cell end table 

Jadi, terbukti bahwa 2 space cos space straight theta times sin space 3 straight theta equals sin space 2 straight theta space open parentheses 2 space cos space 2 straight theta plus 1 close parentheses.

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