Question

一道高一计算题！！！急求解！！！！

cos π/15 * cos 2π/15 * cos4π/15 * cos8π/15 =？

Answer 1

将分母看做1得到(cos π/15 * cos 2π/15 * cos4π/15 * cos8π/15 )/1
=(16sinπ/15 *cos 2π/15 * cos4π/15 * cos8π/15 )/16sinπ/15
=(8sin2π/15*cos 2π/15 * cos4π/15 * cos8π/15) /16sinπ/15
=(4sin4π/15 * cos4π/15 * cos8π/15) /16sinπ/15
=(2sin8π/15 * cos8π/15) /16sinπ/15
=(sin16π/15 )/16sinπ/15
=(-sinπ/15 )/16sinπ/15 =-1/16

Answer 2

=[1/(sin π/15)]*sinπ/15 *cos π/15 * cos 2π/15 * cos4π/15 * cos8π/15
=[1/(sin π/15)]*(1/2)*sin2π/15 * cos 2π/15 * cos4π/15 * cos8π/15
=[1/(sin π/15)]*(1/4)*sin4π/15 * cos4π/15 * cos8π/15
=[1/(sin π/15)]*(1/8)*sin8π/15 * cos8π/15
=[1/(sin π/15)]*(1/16)*sin16π/15
=[1/(sin π/15)]*(1/16)*sin(π+π/15 )
=[1/(sin π/15)]*(1/16)*sinπ/15
=1/16