Pertanyaan

Nilai dari tan 4 3 π + cos 4 5 π − sin 2 3 π tan 4 π − sin 3 2 π + cos 3 4 π adalah...

Nilai dari $\frac{tan \frac{π}{4} - sin \frac{2 π}{3} + cos \frac{4 π}{3}}{tan \frac{3 π}{4} + cos \frac{5 π}{4} - sin \frac{3 π}{2}}$ adalah...

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

nilai dari adalah .

nilai dari $fraction numerator tan begin display style straight pi over 4 end style minus sin begin display style fraction numerator 2 straight pi over denominator 3 end fraction end style plus cos begin display style fraction numerator 4 straight pi over denominator 3 end fraction end style over denominator tan begin display style fraction numerator 3 straight pi over denominator 4 end fraction end style plus cos begin display style fraction numerator 5 straight pi over denominator 4 end fraction end style minus sin begin display style fraction numerator 3 straight pi over denominator 2 end fraction end style end fraction$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 plus 2 square root of 3 over denominator 2 square root of 2 end fraction end cell end table$ .

Pembahasan

Diketahui , maka Jadi, nilai dari adalah .

Diketahui straight pi equals 180 , maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator tan begin display style straight pi over 4 end style minus sin begin display style fraction numerator 2 straight pi over denominator 3 end fraction end style plus cos begin display style fraction numerator 4 straight pi over denominator 3 end fraction end style over denominator tan begin display style fraction numerator 3 straight pi over denominator 4 end fraction end style plus cos begin display style fraction numerator 5 straight pi over denominator 4 end fraction end style minus sin begin display style fraction numerator 3 straight pi over denominator 2 end fraction end style end fraction end cell equals cell fraction numerator tan begin display style 180 over 4 end style minus sin begin display style fraction numerator 2 left parenthesis 180 right parenthesis over denominator 3 end fraction end style plus cos begin display style fraction numerator 4 left parenthesis 180 right parenthesis over denominator 3 end fraction end style over denominator tan begin display style fraction numerator 3 left parenthesis 180 right parenthesis over denominator 4 end fraction end style plus cos begin display style fraction numerator 5 left parenthesis 180 right parenthesis over denominator 4 end fraction end style minus sin begin display style fraction numerator 3 left parenthesis 180 right parenthesis over denominator 2 end fraction end style end fraction end cell row blank equals cell fraction numerator tan 45 minus sin begin display style 360 over 3 end style plus cos begin display style 720 over 3 end style over denominator tan begin display style 540 over 4 end style plus cos begin display style 900 over 4 end style minus sin begin display style 540 over 2 end style end fraction end cell row blank equals cell fraction numerator tan 45 minus sin begin display style 120 end style plus cos 240 over denominator tan begin display style 135 end style plus cos begin display style 225 end style minus sin begin display style 270 end style end fraction end cell row blank equals cell fraction numerator 1 minus begin display style 1 half end style square root of 3 plus open parentheses negative begin display style 1 half end style close parentheses over denominator negative 1 plus open parentheses negative begin display style 1 half end style square root of 2 close parentheses minus left parenthesis negative 1 right parenthesis end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style minus begin display style 1 half end style square root of 3 over denominator negative begin display style 1 half end style square root of 2 end fraction end cell row blank equals cell open parentheses 1 half minus 1 half square root of 3 close parentheses space divided by space fraction numerator negative square root of 2 over denominator 2 end fraction end cell row blank equals cell open parentheses 1 half minus 1 half square root of 3 close parentheses space cross times fraction numerator 2 over denominator negative square root of 2 end fraction end cell row blank equals cell fraction numerator 2 over denominator negative 2 square root of 2 end fraction minus fraction numerator 2 square root of 3 over denominator negative 2 square root of 2 end fraction end cell row blank equals cell negative fraction numerator 2 plus 2 square root of 3 over denominator 2 square root of 2 end fraction end cell end table$

Jadi, nilai dari $fraction numerator tan begin display style straight pi over 4 end style minus sin begin display style fraction numerator 2 straight pi over denominator 3 end fraction end style plus cos begin display style fraction numerator 4 straight pi over denominator 3 end fraction end style over denominator tan begin display style fraction numerator 3 straight pi over denominator 4 end fraction end style plus cos begin display style fraction numerator 5 straight pi over denominator 4 end fraction end style minus sin begin display style fraction numerator 3 straight pi over denominator 2 end fraction end style end fraction$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 plus 2 square root of 3 over denominator 2 square root of 2 end fraction end cell end table$ .

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Fitria Ramadhani

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