Pertanyaan

Buktikan identitas trigonometri berikut. tanAcos 4 A + cotan A sin 4 A = sin A cos A

Buktikan identitas trigonometri berikut.

$tan A cos^{4} A + cotan A sin^{4} A = sin A cos A$

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I. Kumaralalita

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Pembahasan

Ingat identitas trigonometri berikut : Dengan demikian, Dengan demikian, terbukti bahwa .

Ingat identitas trigonometri berikut :

$tan space A equals fraction numerator sin space A over denominator cos space A end fraction cos squared A plus sin squared A equals 1$

Dengan demikian,

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell tan space straight A space cos to the power of 4 space straight A plus cotan space straight A space sin to the power of 4 space straight A end cell row blank equals cell open parentheses fraction numerator sin space straight A over denominator cos space straight A end fraction close parentheses cos to the power of 4 space straight A plus open parentheses fraction numerator cos space straight A over denominator sin space straight A end fraction close parentheses sin to the power of 4 space straight A end cell row blank equals cell sin space straight A space cos cubed space straight A plus cos space straight A space sin cubed space straight A end cell row blank equals cell sin space straight A space cos space straight A open parentheses cos squared space straight A plus sin squared space straight A close parentheses end cell row blank equals cell sin space straight A space cos space straight A times 1 end cell row blank equals cell sin space straight A space cos space straight A end cell end table$

Dengan demikian, terbukti bahwa