Pertanyaan

Diketahui nilai dari a x cos ∅ + b y sin ∅ = 1 dan a x sin ∅ − b y cos ∅ = − 1 . Hasil dari ( a 2 x 2 + b 2 y 2 ) = ...

Diketahui nilai dari $\frac{x}{a} cos \emptyset + \frac{y}{b} sin \emptyset = 1$ dan $\frac{x}{a} sin \emptyset - \frac{y}{b} cos \emptyset = - 1$ . Hasil dari $(\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}}) = ...$

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Ingat! Diketahui nilai dari dan . Jumlahkan persamaan (1) dan (2), maka: Jadi, jawaban yang tepat adalah E.

Ingat!

Diketahui nilai dari x over a cos empty set plus y over b sin empty set equals 1 dan x over a sin empty set minus y over b cos empty set equals negative 1 .

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell x over a cos empty set plus y over b sin empty set end cell equals 1 row cell open parentheses x over a cos empty set plus y over b sin empty set close parentheses squared end cell equals cell 1 squared end cell row cell x squared over a squared cos squared empty set plus 2 fraction numerator x y over denominator a b end fraction sin empty set space cos empty set plus y squared over b squared sin squared empty set end cell equals cell 1 space... space left parenthesis 1 right parenthesis end cell end table end style$

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell x over a sin empty set minus y over b cos empty set end cell equals cell negative 1 end cell row cell open parentheses x over a sin empty set minus y over b cos empty set close parentheses squared end cell equals cell open parentheses negative 1 close parentheses squared end cell row cell x squared over a squared sin squared empty set minus 2 fraction numerator x y over denominator a b end fraction sin empty set space cos empty set plus y squared over b squared cos squared empty set end cell equals cell 1 space... space left parenthesis 2 right parenthesis end cell end table end style$

Jumlahkan persamaan (1) dan (2), maka:

$begin mathsize 12px style table row cell table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell x squared over a squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank empty set end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x y over denominator a b end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank empty set end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank empty set end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell y squared over b squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank empty set end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table 1 end cell row cell table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell x squared over a squared end cell end table sin squared table attributes columnalign right center left columnspacing 0px end attributes row blank blank empty set end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x y over denominator a b end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank empty set end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank empty set end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell y squared over b squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank empty set end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 space space space space space plus end cell end table end cell row cell table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell x squared over a squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis cos end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell empty set plus sin squared empty set right parenthesis plus y squared over b squared left parenthesis sin squared empty set plus end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row cell empty set right parenthesis end cell equals 2 end table end cell end table space end style$

Jadi, jawaban yang tepat adalah E.