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Nilai cot 105° tan 15°=…

Trigonometri Matematika · PTN hard

Nilai cot⁡105∘ tan⁡15∘=…\cot 105^\circ\,\tan 15^\circ=\ldots

  1. A
    −7+43-7+4\sqrt{3}
    ✓
  2. B
    7+437+4\sqrt{3}
  3. C
    7−437-4\sqrt{3}
  4. D
    −7−43-7-4\sqrt{3}
  5. E
    −7+23-7+2\sqrt{3}

Kunci jawaban

A

Penjelasan singkat

tan⁡15∘=2−3\tan15^\circ=2-\sqrt3 dan cot⁡105∘=3−2\cot105^\circ=\sqrt3-2. Hasil kali =(3−2)(2−3)=43−7=(\sqrt3-2)(2-\sqrt3)=4\sqrt3-7.

tan⁡15∘=2−3\tan15^\circ=2-\sqrt3. Karena tan⁡105∘=−(2+3)\tan105^\circ=-(2+\sqrt3) maka cot⁡105∘=1tan⁡105∘=−(2−3)=3−2\cot105^\circ=\frac{1}{\tan105^\circ}=-(2-\sqrt3)=\sqrt3-2.

cot⁡105∘tan⁡15∘=(3−2)(2−3)=43−7=−7+43\cot105^\circ\tan15^\circ=(\sqrt3-2)(2-\sqrt3)=4\sqrt3-7=-7+4\sqrt3. Jawabannya A.

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