Question

How the value of (sin 72)÷ (sin 36) is equal to √5+1÷2​
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Answer 1

Answer:

First simplify

$\frac{ \sin(72) }{ \sin(36) } = \frac{2 \sin(36) \cos(36) }{ \sin(36) } = 2 \cos(36) = 2 \cos( \frac{\pi}{5} )$

all we need is cos π/5 .

And

$\cos( \frac{\pi}{5} ) = \frac{ \sqrt{5} + 1 }{4}$

It is well known result . Which also can derived taking x = π / 5 , or π = 5x

Take cos

$\cos(5x) = \cos(\pi) \\observe \: \: cos4x = - \cos(x) \\ \cos(5x) = \cos(x) ( - 2 \cos(2x) + 2 \cos(4x) + 1)$