Question

求三角函数的化简！题目如图

Answer 1

解：
(sinx)^3 = sinx (sinx)^2 = sinx * { [ 1-cos(2x)]/2 } = (1/2) sinx - (1/2) sinx *cos(2x)
= (1/2) sinx - (1/4) [sin (3x) - sin(x) ]
= (3/4) sinx - (1/4) [sin (3x)
sinx * cosx = (1/2) * sin(2x)
y = (3/4) sinx - (1/4) [sin (3x) + (1/2) * sin(2x)
= (3/4) sinx + (1/2) * sin(2x) - (1/4) [sin (3x)

追问

为什么(1/2) sinx *cos(2x)
= (1/4) [sin (3x) - sin(x) ]

追答

2 cosa * sin b = sin( a + b) - sin(a-b)

2 cosa * sin b = sin( a + b) - sin(a-b)