Pertanyaan

Buktikanlah setiap identitas trigonometri berikut ini. cos 4 x ( 1 − tan 4 x ) = cos 2 x − sin 2 x

Buktikanlah setiap identitas trigonometri berikut ini.

$cos^{4} x (1 - tan^{4} x) = cos^{2} x - sin^{2} x$

N. Indah

Master Teacher

Mahasiswa/Alumni Universitas Diponegoro

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

Terbukti.

Dengan demikian, terbukti bahwa .