1、考点规范练19同角三角函数的基本关系及诱导公式一、基础巩固1.若-2,2,sin =-35,则cos(-)等于()A.-45B.45C.35D.-352.已知tan(-)=34,且2,32,则sin(+2)等于()A.45B.-45C.35D.-353.sin296+cos-293-tan254等于()A.0B.12C.1D.-124.(多选)若sin =45,且为锐角,则下列结论中正确的有()A.tan=43B.cos=35C.sin+cos =85D.sin-cos =-155.已知sin-2cos3sin+5cos=-5,则tan 的值为()A.-2B.2C.2316D.-23166.已
2、知sin(-)=-2sin2+,则sin cos 等于()A.25B.-25C.25或-25D.-157.已知cos512+=13,且-2,则cos12-等于()A.223B.-13C.13D.-2238.若(0,),sin(-)+cos =23,则sin -cos 的值为()A.23B.-23C.43D.-439.已知cos =-35(2),则sin =;tan(-)=.10.若f(cos x)=cos 2x,则f(sin 15)=.11.已知为第二象限角,则cos 1+tan2+sin 1+1tan2=.12.已知kZ,则sin(k-)cos(k-1)-sin(k+1)+cos(k+)=.
3、二、综合应用13.已知2tan sin =3,-2log2x的解集为.考点规范练19同角三角函数的基本关系及诱导公式1.B因为-2,2,sin=-35,所以cos=45,即cos(-)=45.2.Btan(-)=34,tan=34.又2,32,32.sin+2=cos=-45.3.A原式=sin4+56+cos-10+3-tan6+4=sin56+cos3-tan4=12+12-1=0.4.ABsin=45,且为锐角,cos=1-sin2=1-452=35,故B正确;tan=sincos=43,故A正确;sin+cos=45+35=75,sin-cos=45-35=15,故C,D错误.5.D由
4、题意可知cos0,则sin-2cos3sin+5cos=tan-23tan+5=-5,解得tan=-2316.6.Bsin(-)=-2sin2+,sin=-2cos,tan=-2.sincos=sincossin2+cos2=tan1+tan2=-25,故选B.7.Dcos512+=sin12-=13,且-2,71212-1312,cos12-=-1-sin212-=-223.8.C由诱导公式得sin(-)+cos=sin+cos=23,平方得(sin+cos)2=1+2sincos=29,则2sincos=-790,故(sin-cos)2=1-2sincos=169,又(0,),所以sin-
5、cos=43.9.-45-43因为cos=-35(2),所以32,所以sin0,cos0,所以cos1|cos|+sin1|sin|=-1+1=0,即原式等于0.12.-1当k=2n(nZ)时,原式=sin(2n-)cos(2n-1)-sin(2n+1)+cos(2n+)=sin(-)cos(-)sin(+)cos=-sin(-cos)-sincos=-1;当k=2n+1(nZ)时,原式=sin(2n+1)-cos(2n+1-1)-sin(2n+1+1)+cos(2n+1)+=sin(-)cossincos(+)=sincossin(-cos)=-1.综上,原式=-1.13.B2tansin=3,2sin2cos=3,即2cos2+3cos-2=0.又-2log2x,即1log2x,解得0x2.
