求值:已知cosx=1/3,-π/2

求值:已知cosx=1/3,-π/2

首先,tanx=-2√2.
其次,tan(-x-π)sin(2π+x) / cos(-x)tanx
=-tanx sinx/(cosx tanx)
=-tanx
=2√2

画图是最好的办法，就是左右上下平移的事

cosx = 1/3
tanx = -2√2/3
tan(-x-π)sin(2π+x) / [cos(-x)tanx ]
= tan-(π+x)sin(2π+x) / [cos(-x)tanx ]
= -tanxsinx/[cosxtanx]
= -sinx/cosx
=-tanx
= 2√2/3