Pertanyaan

Tunjukkan kebenaran identitas trigonometri berikut. f. ( sin 2 A − cos 2 A ) ( sin 2 A + cos 2 A ) = cos 2 A ( tan 2 A − 1 )

Tunjukkan kebenaran identitas trigonometri berikut.

f. $(sin^{2} A - cos^{2} A) (sin^{2} A + cos^{2} A) = cos^{2} A (tan^{2} A - 1)$

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E. Lestari

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Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa open parentheses sin squared A minus cos to the power of 2 space end exponent A close parentheses open parentheses sin squared A plus cos to the power of 2 space end exponent A close parentheses equals cos squared A open parentheses tan squared A minus 1 close parentheses

open parentheses sin squared A minus cos to the power of 2 space end exponent A close parentheses open parentheses sin squared A plus cos to the power of 2 space end exponent A close parentheses equals cos squared A open parentheses tan squared A minus 1 close parentheses

Pembahasan

Ingat! Akan ditunjukkan bahwa Perhatikan perhitungan berikut ini! Dengan demikian terbukti bahwa .

Ingat!

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

Akan ditunjukkan bahwa

open parentheses sin squared A minus cos to the power of 2 space end exponent A close parentheses open parentheses sin squared A plus cos to the power of 2 space end exponent A close parentheses equals cos squared A open parentheses tan squared A minus 1 close parentheses

Perhatikan perhitungan berikut ini!

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses sin squared A minus cos to the power of 2 space end exponent A close parentheses open parentheses sin squared A plus cos to the power of 2 space end exponent A close parentheses end cell row blank equals cell open parentheses sin squared A minus cos to the power of 2 space end exponent A close parentheses times 1 end cell row blank equals cell open parentheses sin squared A minus cos to the power of 2 space end exponent A close parentheses times fraction numerator cos squared A over denominator cos squared A end fraction end cell row blank equals cell fraction numerator open parentheses sin squared A minus cos to the power of 2 space end exponent A close parentheses over denominator cos squared A end fraction times cos squared A end cell row blank equals cell cos squared A times fraction numerator open parentheses sin squared A minus cos to the power of 2 space end exponent A close parentheses over denominator cos squared A end fraction end cell row blank equals cell cos squared A times open parentheses fraction numerator sin squared A over denominator cos squared A end fraction minus fraction numerator cos squared A over denominator cos squared A end fraction close parentheses end cell row blank equals cell cos squared A open parentheses tan squared minus 1 close parentheses end cell end table$

Dengan demikian terbukti bahwa open parentheses sin squared A minus cos to the power of 2 space end exponent A close parentheses open parentheses sin squared A plus cos to the power of 2 space end exponent A close parentheses equals cos squared A open parentheses tan squared A minus 1 close parentheses .