- 函数求证:(tan5x+tan3x)/cos2xcos4x=4(
- 求证:(tan5x+tan3x)/c2xcos4x=4(tan5x-tan3x)
- 证明:
左边=(tan5x+tan3x )/c2xcos4x
=(sin5x /cos5x +sin3x /cos3x )/cos2xcos4x
=(sin5xcos3x +sin3xcos5x )/cos2xcos3xcos4xcos5x
=sin8x /cos2xcos3xcos4xcos5x
=2sin4xcos4x /cos2xcos3xcos4xcos5x
=4sin2xcos2x /cos2xcos3xcos5x
=4sin2x /cos3xcos5x
右边=4(tan5x -tan3x )
=4(sin5x/cos5x -sin3x/cos3x )
=4(sin5xcos3x -sin3xcos5x )/cos3xcos5x
=4sin2x /cos3xcos5x
所以,(tan5x+tan3x)/cos2xcos4x=4(tan5x-tan3x)