Pertanyaan

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

Buktikan:

a. $2 sin (\frac{1}{4} π + α) sin (\frac{3}{4} π + α) = cos 2 α$

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Jawaban terverifikasi

Jawaban

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

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

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:

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 .