find the value of cos18
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5 * 18 = 90
so, 3 * 18 = 90 - 2 * 18
Cos (3 * 18) = Cos (90 - 2 * 18)
4 Cos³ 18 - 3 Cos 18 = Sin 2 * 18 = 2 Sin 18 Cos 18
As Cos 18 ≠ 0, cancelling the term
4 Cos² 18 - 3 = 2 Sin 18
4 - 4 Sin²18 - 3 = 2 Sin 18
4 Sin² 18 + 2 Sin 18 - 1 = 0
Sin 18 = (-2 +-√(4+16 )/8 = (√5 - 1) / 4 as sin 18 is positive.
Cos 18 = √(16 - 5 -1 + 2√5) / 4 = √(10+2√5) / 4
so, 3 * 18 = 90 - 2 * 18
Cos (3 * 18) = Cos (90 - 2 * 18)
4 Cos³ 18 - 3 Cos 18 = Sin 2 * 18 = 2 Sin 18 Cos 18
As Cos 18 ≠ 0, cancelling the term
4 Cos² 18 - 3 = 2 Sin 18
4 - 4 Sin²18 - 3 = 2 Sin 18
4 Sin² 18 + 2 Sin 18 - 1 = 0
Sin 18 = (-2 +-√(4+16 )/8 = (√5 - 1) / 4 as sin 18 is positive.
Cos 18 = √(16 - 5 -1 + 2√5) / 4 = √(10+2√5) / 4
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