一、基本公式:sin2=cos2=tan2=2sincos(S2)cos2-sin2(C2)2tan/(1-tan2)(T2)利用sin2+cos2=1,公式C2还可以变形为:cos2=1-2sin2或cos2=2cos2-1二、例题:例1已知sin=5/13,∈(/2,),求sin2,cos2,tan2的值。解:∵sin=5/13,∈(/2,),∴cos=13121351sin122于是:sin2=2sincos=16912013121352cos2=1-2sin2=169119135212tan2=1191201191691691202cos2sin例2求下列各式的值。(1)sin3750sin1050-4cos222030`+2(2)0015tan1115tan11解(1)原式=sin150sin750-2(cos222030`-1)=sin150cos150-2cos450=24122230sin210(2)原式=3330tan15tan115tan215tan115tan115tan115tan100200000例3求证1+2cos2x-cos2x=2证明:左边=1+2cos2x-(2cos2x-1)=1+2cos2x-2cos2x+1=2=右边∴等式成立例4利用三角公式化简)10tan31(50sin00原式=)10cos10sin31(50sin000000010cos10sin2310cos21250sin00000010cos10sin30cos10cos30sin50sin200010cos40sin40cos2110cos10cos10cos80sin0000