Did you mean sin54-sin18=1/2 ?
cos36 - sin18
= 1-2sin^2 18 - sin18
= 1-2[(1/4)(sqrt5 - 1)]^2 - (1/4)(sqrt5 - 1), since sin18 = (1/4)(sqrt5 - 1)
= 1 - (1/8)(6-2sqrt5) - (1/4)(sqrt5 - 1)
= 1 - 3/4 + 1/4
= 2/4
= 1/2
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