Question

sin6°cos24°•sin78°cos48°的值等于

sin6°cos24°•sin78°cos48°的值等于
A.- 1/16 B.- 1/8 C.1/16 D.1/8

Answer 1

sin6°cos24°=(1/2)*(sin30°+sin18°)
sin78°cos48°=(1/2)*(sin30°+sin126°)=(1/2)*(sin30°+sin54°)
(根据和差化积公式.)
所以原式
=(1/4)*(1/2+sin18°)*(1/2+sin54°)
=(1/4)*[1/4+(1/2)*(sin18°+sin54°)+sin18°*sin54°]
=(1/4)*[1/4+sin36°cos18°-(1/2)cos72°cos36°]
=(1/4)*(1/4+0) (利用sin18°=(根号5-1)/4)
=1/16.

附:和差化积公式参见课本.

Answer 2

C