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Buktikanlah setiap identitas trigonometri berikut ini.


begin mathsize 14px style cos to the power of 4 x left parenthesis 1 minus tan to the power of 4 x right parenthesis equals cos squared x minus sin squared x end style

 

N. Indah

Master Teacher

Mahasiswa/Alumni Universitas Diponegoro

Jawaban terverifikasi

Jawaban

terbukti bahwa begin mathsize 14px style cos to the power of 4 x left parenthesis 1 minus tan to the power of 4 x right parenthesis equals cos squared x minus sin squared x end style.

Pembahasan

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell cos to the power of 4 space x space open parentheses 1 minus tan to the power of 4 space x close parentheses end cell equals cell cos to the power of 4 space x space open parentheses 1 minus fraction numerator sin to the power of 4 space x over denominator cos to the power of 4 space x end fraction close parentheses end cell row blank equals cell cos to the power of 4 space x space minus space sin to the power of 4 space x end cell row blank equals cell open parentheses cos squared space x plus sin squared space x close parentheses open parentheses cos squared space x minus sin squared space x close parentheses end cell row cell cos to the power of 4 space x space open parentheses 1 minus tan to the power of 4 space x close parentheses end cell equals cell cos squared space x minus sin squared space x end cell end table end style

Terbukti.

Dengan demikian, terbukti bahwa begin mathsize 14px style cos to the power of 4 x left parenthesis 1 minus tan to the power of 4 x right parenthesis equals cos squared x minus sin squared x end style.

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