Pertanyaan

Buktikan bahwa cs c 6 x ( 1 − cos 6 x ) − 1 = 3 co t 2 x cs c 2 x

Buktikan bahwa $cs c^{6} x (1 - cos^{6} x) - 1 = 3 co t^{2} x cs c^{2} x$

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S. Indah

Master Teacher

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Jawaban

terbukti bahwa .

terbukti bahwa c s c to the power of 6 x left parenthesis 1 minus cos to the power of 6 x right parenthesis minus 1 equals 3 space c o t squared x space c s c squared x

c s c to the power of 6 x left parenthesis 1 minus cos to the power of 6 x right parenthesis minus 1 equals 3 space c o t squared x space c s c squared x

Pembahasan

Ingat! Akan dibuktikan: Bukti: Dengan demikian, terbukti bahwa .

Ingat!

$table attributes columnalign right center left columnspacing 0px end attributes row cell c o t space x end cell equals cell fraction numerator cos space x over denominator sin space x end fraction end cell row cell c s c space x end cell equals cell fraction numerator 1 over denominator sin space x end fraction end cell row cell sin squared x plus cos squared x end cell equals 1 end table$

Akan dibuktikan: c s c to the power of 6 x left parenthesis 1 minus cos to the power of 6 x right parenthesis minus 1 equals 3 space c o t squared x space c s c squared x

Bukti:

$table attributes columnalign right center left columnspacing 0px end attributes row cell c s c to the power of 6 x left parenthesis 1 minus cos to the power of 6 x right parenthesis minus 1 end cell equals cell c s c to the power of 6 x minus cos to the power of 6 x space c s c to the power of 6 x minus 1 end cell row blank equals cell fraction numerator c s c to the power of 6 x minus cos to the power of 6 x over denominator sin to the power of 6 x minus 1 end fraction end cell row blank equals cell fraction numerator 1 over denominator sin to the power of 6 x end fraction minus fraction numerator cos to the power of 6 x over denominator sin to the power of 6 x end fraction minus fraction numerator sin to the power of 6 x over denominator sin to the power of 6 x end fraction end cell row blank equals cell fraction numerator 1 minus cos to the power of 6 x minus sin to the power of 6 x over denominator sin to the power of 6 x end fraction end cell row blank equals cell fraction numerator 1 minus left parenthesis cos to the power of 6 x plus sin to the power of 6 x right parenthesis over denominator sin to the power of 6 x end fraction end cell row blank equals cell fraction numerator 1 minus left parenthesis left parenthesis cos squared x plus sin squared x right parenthesis cubed minus 3 space cos to the power of 4 end exponent x space sin squared x minus 3 space cos squared x space sin to the power of 4 x right parenthesis over denominator sin to the power of 6 x end fraction end cell row blank equals cell fraction numerator 1 minus left parenthesis 1 cubed minus 3 space cos to the power of 4 x space sin squared x minus 3 space cos squared x space sin to the power of 4 x right parenthesis over denominator sin to the power of 6 x end fraction end cell row blank equals cell fraction numerator 3 space cos to the power of 4 x space sin squared x plus 3 space cos squared x space sin to the power of 4 x over denominator sin to the power of 6 x end fraction end cell row blank equals cell fraction numerator 3 space cos squared x space sin squared x left parenthesis cos squared x plus sin squared x right parenthesis over denominator sin to the power of 6 x end fraction end cell row blank equals cell fraction numerator 3 space cos squared x space sin squared x left parenthesis 1 right parenthesis over denominator sin to the power of 6 x end fraction end cell row blank equals cell fraction numerator 3 space cos squared x over denominator sin to the power of 4 x end fraction end cell row blank equals cell fraction numerator 3 space cos squared x over denominator sin squared x space sin squared x end fraction end cell row blank equals cell 3 fraction numerator cos squared x over denominator sin squared x end fraction times fraction numerator 1 over denominator sin squared x end fraction end cell row blank equals cell 3 space c o t squared x space c s c squared x end cell end table$

Dengan demikian, terbukti bahwa c s c to the power of 6 x left parenthesis 1 minus cos to the power of 6 x right parenthesis minus 1 equals 3 space c o t squared x space c s c squared x .

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