Pertanyaan

Hitunglah hasil dari: b. cos 2 22 5 ∘ tan 2 22 5 ∘ + cos 24 0 ∘ + sin 33 0 ∘

Hitunglah hasil dari:

b. $\frac{tan ^{2} 22 5 ^{\circ} + cos 24 0 ^{\circ} + sin 33 0 ^{\circ}}{cos ^{2} 22 5 ^{\circ}}$

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Klaim

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

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$fraction numerator tan squared space 225 degree plus cos space 240 degree plus sin space 330 degree over denominator cos squared space 225 degree end fraction equals 0$ .

Pembahasan

Perhatikan perbandingan trigonometri sudut-sudut berelasi berikut. Sehingga dapat ditentukan: Selanjutnya dapat ditentukan nilai dari: Dengan demikian, .

Perhatikan perbandingan trigonometri sudut-sudut berelasi berikut.

Sehingga dapat ditentukan:

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 225 degree end cell equals cell tan space 225 degree end cell row blank equals cell tan space open parentheses 270 degree minus 45 degree close parentheses end cell row blank equals cell cot space 45 degree end cell row blank equals cell fraction numerator cos space 45 degree over denominator sin space 45 degree end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style square root of 2 over denominator begin display style 1 half end style square root of 2 end fraction end cell row blank equals 1 row cell cos space 240 degree end cell equals cell cos space open parentheses 270 degree minus 30 degree close parentheses end cell row blank equals cell negative sin space 30 degree end cell row blank equals cell negative 1 half end cell row cell sin space 330 degree end cell equals cell sin space open parentheses 360 degree minus 30 degree close parentheses end cell row blank equals cell negative sin space 30 degree end cell row blank equals cell negative 1 half end cell row cell cos space 225 degree end cell equals cell cos space open parentheses 270 degree minus 45 degree close parentheses end cell row blank equals cell negative sin space 45 degree end cell row blank equals cell negative 1 half square root of 2 end cell end table$

Selanjutnya dapat ditentukan nilai dari:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator tan squared space 225 degree plus cos space 240 degree plus sin space 330 degree over denominator cos squared space 225 degree end fraction end cell equals cell fraction numerator 1 squared plus open parentheses negative begin display style 1 half end style close parentheses plus open parentheses negative begin display style 1 half end style close parentheses over denominator open parentheses negative begin display style 1 half end style square root of 2 close parentheses squared end fraction end cell row blank equals cell fraction numerator 1 minus 1 over denominator begin display style 1 half end style end fraction end cell row blank equals cell fraction numerator 0 over denominator begin display style 1 half end style end fraction end cell row blank equals 0 end table$

Dengan demikian, $fraction numerator tan squared space 225 degree plus cos space 240 degree plus sin space 330 degree over denominator cos squared space 225 degree end fraction equals 0$ .