（1）计算log225•log34•log59+lg0.001-(13)−2（2）已知tanx=2，求值：sin2(5400−x)tan(9000−x)•1tan(4500−x)tan(8100−x)•cos(3600−x)sin(−x)．

Question

（1）计算log₂25•log₃4•log₅9+lg0.001-((1)/(3))−2
（2）已知tanx=2，求值：(sin2(5400−x))/(tan(9000−x))•(1)/(tan(4500−x)tan(8100−x))•(cos(3600−x))/(sin(−x))．

Answer 1

（1）因为log₂25•log₃4•log₅9+lg0.001-((1)/(3))−2
=8log₂5•log₃2•log₅3-3-9
=8-3-9
=-4
（2）(sin2(540°−x))/(tan(900°−x))•(1)/(tan(450°−x)tan(810°−x))•(cos(360°−x))/(sin(−x))
=(sin2x)/(−tanx)•(1)/(cotxcotx)•(cosx)/(−sinx)
=(tan2x)/(tan2x+1)
=(4)/(5)．