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
[tex]Hence,\ Cos\ A=\frac{\sqrt{10+2\sqrt5}}{4}[/tex]
