Question

find the value of: cos18

Answer 1

Let A = 18°           5A = 90°
2A = 90 - 3A
Sin 2A = Sin (90-3A) = Cos 3A

2 Sin A Cos A = 4Cos³ A - 3 Cos A ,  Cancel Cos A as it is not zero.

2 Sin A = 4 Cos² A - 3  = 1 - 4 Sin² A

4 Sin² A + 2 Sin A - 1 = 0 

Solving quadratic equation :   Sin A = (√5 - 1)/4
Sin² A = (1-2Sin A)/4 = (3-√5 )/ 8
Cos² A = (5+√5)/8 

$Hence,\ Cos\ A=\frac{\sqrt{10+2\sqrt5}}{4}$