Question

(+50) KuMat - Kuis Matematika
Trigonometri

Temukan bilangan asli terkecil [tex]n[/tex] yang memenuhi persamaan
[tex]\begin{aligned}\frac{1}{\sin n^\circ}&=\frac{1}{\sin45^\circ\sin46^\circ}+\frac{1}{\sin47^\circ\sin48^\circ}+{\dots}+\frac{1}{\sin133^\circ\sin134^\circ}\end{aligned}[/tex]

Answer 1

Verified answer

Penjelasan dengan langkah-langkah:

TRIGONOMETRI

[tex]\begin{aligned}\frac{1}{\sin n^\circ}&=\frac{1}{\sin45^\circ\sin46^\circ}+\frac{1}{\sin47^\circ\sin48^\circ}+{\dots}+\frac{1}{\sin133^\circ\sin134^\circ}\end{aligned} \\ \\= \frac{1}{\sin45^\circ\sin46^\circ}+\frac{1}{\sin47^\circ\sin48^\circ}+{\dots}+\frac{1}{\sin133^\circ\sin134^\circ} \: \\ \\ = ( \frac{sin \: (46 - 45)^\circ}{sin45^\circ \: sin46^\circ} + \frac{sin(48 - 47)^\circ}{sin47^\circ \: sin48^\circ} + .... + \frac{sin(134 - 133)^\circ}{sin 133^\circ \: sin134^\circ} ) \times \frac{1}{sin \: 1^\circ} \\ \\ = \frac{ ((cot45 - 46 )+ (cot \: 47 - cot48) + .... + (cot \: 133 - cot \: 134)}{sin \: 1^\circ} \\ \\ = \frac{cot \: 45^\circ}{sin \: 1^\circ} \\ \\ [/tex]

[tex] \frac{cot \: 45^\circ}{sin \: 1^\circ} = \frac{1}{sin \: n^\circ} \\ [/tex]

[tex]maka \: n = 1[/tex]

PENJELASAN UNTUK BARIS KETIGA

Sifat TRIGONOMETRI

= ( Sin (A-B))/(SinA.SinB)

= (SinA.CosB)/(SinA.SinB) - (CosA.SinB)/(SinA.SinB)

= Cot B - Cot A

Note : Gambar hanya penjabaran cara mulai dari baris ketiga

Terima kasih atas koreksinya