cos78度+sin78度sin18度

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cos78度+sin78度sin18度cos78度+sin78度sin18度cos78度+sin78度sin18度cos78°+sin78°sin18°=cos(60°+18°)+sin(60°+18

cos78度+sin78度sin18度
cos78度+sin78度sin18度

cos78度+sin78度sin18度
cos78°+sin78°sin18°
=cos(60°+18°)+sin(60°+18°)sin18°
=cos60°cos18°-sin60°sin18°+(sin60°cos18°+cos60°sin18°)sin18°
=(1/2)cos18°-(√3/2)sin18°+(√3/2)cos18°sin18°+(1/2)(sin18°)^2
=(1/2)cos18°-(√3/2)sin18°+(√3/4)sin36°+(1/4)(1-cos36)
=1/4+(1/2)×√(10+2√5)/4-(√3/2)×(√5-1)/4+(√3/4)×√(10-2√5)/4
 +(1/4)×(√5+1)/4
=1/4+√(10+2√5)/8-√3(√5-1)/8+√3(√10-2√5)/16+(√5+1)/16.

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