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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

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