Pertanyaan

Jika x 1 dan x 2 adalah solusi dari cos x sin 2 x 2 sin x cos 2 x + 5 tan x − 7 = 0 , maka adalah ....

Jika $x_{1}$ dan $x_{2}$ adalah solusi dari $\frac{2 sin x cos 2 x}{cos x sin 2 x} + 5 tan x - 7 = 0$ , maka adalah ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Perhatikan bahwa Karena , maka Perhatikan bahwa Jadi, jawaban yang tepat adalah B.

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 sin invisible function application x cos invisible function application 2 x over denominator cos invisible function application x sin invisible function application 2 x end fraction plus 5 tan invisible function application x minus 7 end cell equals 0 row cell 2 times fraction numerator sin invisible function application x over denominator cos invisible function application x end fraction times fraction numerator cos invisible function application 2 x over denominator sin invisible function application 2 x end fraction plus 5 tan invisible function application x minus 7 end cell equals 0 row cell 2 times tan invisible function application x times fraction numerator 1 over denominator tan invisible function application 2 x end fraction plus 5 tan invisible function application x minus 7 end cell equals 0 row cell fraction numerator 2 tan invisible function application x over denominator tan invisible function application 2 x end fraction plus 5 tan invisible function application x minus 7 end cell equals 0 end table end style$

Karena $begin mathsize 14px style tan invisible function application 2 x equals fraction numerator 2 tan invisible function application x over denominator 1 minus tan squared invisible function application x end fraction end style$ , maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 tan invisible function application x over denominator tan invisible function application 2 x end fraction plus 5 tan invisible function application x minus 7 end cell equals 0 row cell fraction numerator 2 tan invisible function application x over denominator fraction numerator 2 tan invisible function application x over denominator 1 minus tan squared invisible function application x end fraction end fraction plus 5 tan invisible function application x minus 7 end cell equals 0 row cell 1 minus tan squared invisible function application x plus 5 tan invisible function application x minus 7 end cell equals 0 row cell negative tan squared invisible function application x plus 5 tan invisible function application x minus 6 end cell equals 0 row cell tan squared invisible function application x minus 5 tan invisible function application x plus 6 end cell equals 0 row cell open parentheses tan invisible function application x minus 2 close parentheses open parentheses tan invisible function application x minus 3 close parentheses end cell equals 0 row cell tan invisible function application x subscript 1 end cell equals cell 2 text atau end text tan invisible function application x subscript 2 equals 3 end cell end table end style$

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan invisible function application open parentheses x subscript 1 minus x subscript 2 close parentheses end cell equals cell fraction numerator tan invisible function application x subscript 1 minus tan invisible function application x subscript 2 over denominator 1 plus tan invisible function application x subscript 1 tan invisible function application x subscript 2 end fraction end cell row blank equals cell fraction numerator 2 minus 3 over denominator 1 plus 2 times 3 end fraction end cell row blank equals cell fraction numerator negative 1 over denominator 1 plus 6 end fraction end cell row blank equals cell negative 1 over 7 end cell end table end style$

Jadi, jawaban yang tepat adalah B.