sin(x－3π/4) cos(x - π/4) = - 1/4,求cos4x
将要用到：2sinAcosB = sin(A+B) + sin(A-B)
和 cos2α = cos²α - sin²α = 1 - 2sin²α
sin(x－3π/4) cos(x - π/4) = 1/2 [sin(2x -π) + sin(-π/2)] = -1/2 [sin2x + 1] = -1/4
===> sin2x = -1/2
cos4x = 1 - 2 sin²2x = 1 - 2 *(1/4) = 1 - 1/2 = 1/2
这样做最简洁的,当然楼上几位的方法也值得参考!