Pertanyaan

Nilai dari ekspresi: cosec [ sin − 1 ( 2 2 ) ] + secan [ cos − 1 ( 2 2 ) ] adalah ....

Nilai dari ekspresi:

$cosec [sin^{- 1} (\frac{2}{2})] + secan [cos^{- 1} (\frac{2}{2})]$

adalah ....

$fraction numerator square root of 2 over denominator 2 end fraction$

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Klaim

Y. Umi

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Ingat! Jika , maka . Jika , maka Misalkan , maka dan , maka . Dengan demikian, Jadi, . Jadi, jawaban yang tepat adalah A.

Ingat!

Jika cos to the power of negative 1 end exponent y equals x , maka cos space x equals y .

Jika sin to the power of negative 1 end exponent y equals x , maka sin space x equals y

Misalkan $sin to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses equals italic x$ , maka $sin space x equals fraction numerator square root of 2 over denominator 2 end fraction$ dan $cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses$ , maka $cos space y equals fraction numerator square root of 2 over denominator 2 end fraction$ . Dengan demikian,

$table attributes columnalign right center left columnspacing 0px end attributes row cell cosec open square brackets sin to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 2 over denominator plus 2 end fraction close parentheses close square brackets plus secan open square brackets cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses close square brackets end cell equals cell cosec space x and secan space y end cell row blank equals cell fraction numerator 1 over denominator sin space italic x end fraction plus fraction numerator 1 over denominator cos space y end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator square root of 2 over denominator 2 end fraction end style end fraction plus fraction numerator 1 over denominator begin display style fraction numerator square root of 2 over denominator 2 end fraction end style end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 2 end fraction plus fraction numerator 2 over denominator square root of 2 end fraction end cell row blank equals cell fraction numerator 4 over denominator square root of 2 end fraction middle dot fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell fraction numerator 4 square root of 2 over denominator 2 end fraction end cell row blank equals cell 2 square root of 2 end cell end table$

Jadi, $cosec open square brackets sin to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses close square brackets plus secan open square brackets cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses close square brackets equals 2 square root of 2$ .

Jadi, jawaban yang tepat adalah A.