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Prove

or, equivalently,

Prove that:

(that is, without computation or tables).

Hint 1. Find closed form expressions for

See Sublime Triangle

Cos 36 degrees

Closed Form for Some Values of Cosine and Sine

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Evaluation once you have the closed form expressions

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The hints below may be useful for finding closed form expressions OR for approaching the problem algebraically.

Hint 2. Consider the isosceles triangle with angles 36, 72, 72.

See Sublime Triangle.

Hint 3. Consider trigonometric identities for half angles and double angles.

 

 

 

Hint 4. Consider the equation

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