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Pertanyaan

Jika a x ​ = cotan γ dan y = b cosec γ , tunjukkan bahwa: a 2 x 2 ​ − b 2 y 2 ​ = − 1

Jika  dan , tunjukkan bahwa: 

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E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa x squared over a squared minus y squared over b squared equals negative 1.

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Pembahasan

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

Ingat!

1 plus cotan squared x equals cosec squared x

Diketahui

table attributes columnalign right center left columnspacing 0px end attributes row cell x over a end cell equals cell cotan space gamma rightwards arrow x equals a space cotan space gamma end cell row y equals cell b space cosec space gamma end cell end table

Akan ditunjukkan bahwa

x squared over a squared minus y squared over b squared equals negative 1

Perhatikan perhitungan berikut ini!

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared over a squared minus y squared over b squared end cell equals cell open parentheses a space cotan space gamma close parentheses squared over a squared minus open parentheses b space cos e c space gamma close parentheses squared over b squared end cell row blank equals cell fraction numerator up diagonal strike a squared end strike space cotan squared gamma over denominator up diagonal strike a squared end strike end fraction minus fraction numerator up diagonal strike b squared end strike space cos e c squared gamma over denominator up diagonal strike b squared end strike end fraction end cell row blank equals cell cotan squared gamma minus cos e c squared gamma end cell row blank equals cell cotan squared gamma minus open parentheses 1 plus cotan squared gamma close parentheses end cell row blank equals cell cotan squared gamma minus 1 minus cotan squared gamma end cell row blank equals cell cotan squared gamma minus cotan squared gamma minus 1 end cell row blank equals cell 0 minus 1 end cell row blank equals cell negative 1 end cell end table

Dengan demikian terbukti bahwa x squared over a squared minus y squared over b squared equals negative 1.

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