Let A1-A2-An be vertices of an n sided regular polygon such that 1A1 A2 - 1A1 A3 - 1A1 A4

A_1A_2 = mod of A_1A_2 = #160;|A_1A_2| |A_1A_r|^2 = |z_1|^2 [2 2 cos #160;2(r 1) πn] = a^2 · 4 sin^2 2(r ...

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Complementary Trigonometric Ratios

Let A1,A2,....

Question

Let $A_{1}, A_{2}, . . . ., A_{n}$ be vertices of an n sided regular polygon such that
$\frac{1}{A_{1} A_{2}} = \frac{1}{A_{1} A_{3}} + \frac{1}{A_{1} A_{4}}$

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A_{1}, A_{2}, . . . . A_{n}

n -

\frac{1}{A_{1} A_{2}} = \frac{1}{A_{1} A_{3}} + \frac{1}{A_{1} A_{4}}

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A_{1}, A_{2}, A_{3} . . . A_{n}

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| O A_{1} | = 1

| A_{1} A_{2} | | A_{1} A_{3} | . . . . | A_{1} A_{n} | = n

A_{1}, A_{2}, \dots, A_{n}

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a = | A_{1} A_{2} |^{2} + | A_{1} A_{3} |^{2} + \dots | A_{1} A_{n} |^{2},

b = | A_{1} A_{2} | | A_{1} A_{3} | \dots | A_{1} A_{n} |,

\frac{a}{b} =

A_{1}, A_{2}, A_{3} \dots A_{n}

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O

A_{1}, A_{2}, A_{3} \dots A_{n}

z_{1}, z_{2}, z_{3} \dots z_{n}

O A_{1} = O A_{2} = \dots = O A_{n} = 1

A_{1} A_{j} (j = 2, 3, \dots, n)

A_{1} A_{2} A_{3} . . . A_{n}

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\frac{1}{A_{1} A_{2}} = \frac{1}{A_{1} A_{3}} + \frac{1}{A_{1} A_{4}},

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