Pertanyaan

cos 3 0 ∘ tan 6 0 ∘ − tan 4 5 ∘ sin 9 0 ∘ sama dengan ....

$\frac{tan 6 0 ^{\circ}}{cos 3 0 ^{\circ}} - \frac{sin 9 0 ^{\circ}}{tan 4 5 ^{\circ}}$ sama dengan ....

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Pembahasan

Tabel trigonometri sudut istimewa sebagai berikut. Berdasarkan tabel diatas diperoleh: Dengan demikian, .

Tabel trigonometri sudut istimewa sebagai berikut.

Berdasarkan tabel diatas diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator tan space 60 degree over denominator cos space 30 degree end fraction minus fraction numerator sin space 90 degree over denominator tan space 45 degree end fraction end cell equals cell fraction numerator square root of 3 over denominator begin display style 1 half square root of 3 end style end fraction minus fraction numerator 1 over denominator begin display style 1 half end style square root of 2 end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style 1 half end style end fraction minus fraction numerator 2 over denominator square root of 2 end fraction end cell row blank equals cell 2 minus fraction numerator 2 over denominator square root of 2 end fraction end cell row blank equals cell fraction numerator 2 square root of 2 over denominator square root of 2 end fraction minus fraction numerator 2 over denominator square root of 2 end fraction end cell row blank equals cell fraction numerator 2 square root of 2 minus 2 over denominator square root of 2 end fraction end cell row blank equals cell fraction numerator 2 square root of 2 minus 2 over denominator square root of 2 end fraction times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell fraction numerator open parentheses 2 square root of 2 minus 2 close parentheses square root of 2 over denominator 2 end fraction end cell row blank equals cell fraction numerator 2 times 2 minus 2 square root of 2 over denominator 2 end fraction end cell row blank equals cell fraction numerator 4 minus 2 square root of 2 over denominator 2 end fraction end cell row blank equals cell fraction numerator 2 open parentheses 2 minus square root of 2 close parentheses over denominator 2 end fraction end cell row blank equals cell 2 minus square root of 2 end cell end table$

Dengan demikian, $table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator tan space 60 degree over denominator cos space 30 degree end fraction minus fraction numerator sin space 90 degree over denominator tan space 45 degree end fraction end cell equals cell 2 minus square root of 2 end cell end table$ .