2019_2020学年高中数学第五章两角和与差的正弦、余弦、正切公式课后篇巩固提升新人教A版.docx

第2课时两角和与差的正弦、余弦、正切公式课后篇巩固提升基础巩固1.sin 35cos 5-cos 35sin 5=()A.12B.1C.2D.2sin 40解析sin35cos5-cos35sin5=sin(35-5)=sin30=12.答案A2.若sin6-=cos6+,则tan =()A.-1B.0C.12D.1解析由已知得12cos-32sin=32cos-12sin,因此1-32sin=3-12cos,于是tan=-1.答案A3.若tan(+)=25,tan(-)=14,则tan 2=()A.16B.2213C.322D.1318解析tan2=tan(+)+(-)=tan(+)+tan(-)1-tan(+)tan(-)=25+141-2514=1318.答案D4.sin(+75)+cos(+45)-3cos(+15)的值等于()A.1B.1C.-1D.0解析原式=sin(+45)+30+cos(+45)-3cos(+45)-30=32sin(+45)+12cos(+45)+cos(+45)-332cos(+45)+12sin(+45)=32sin(+45)+32cos(+45)-32cos(+45)-32sin(+45)=0.答案D5.设0,2,0,2,且tan =1+sincos,则()A.3-=2B.3+=2C.2-=2D.2+=2解析由tan=1+sincos,得sincos=1+sincos,得sincos-cossin=cos,sin(-)=sin2-.又0,2,0,2,故-=2-,即2-=2.答案C6.化简:sin(-150)+cos(-120)cos=.解析原式=sincos150-cossin150+coscos120+sinsin120cos=-32sin-12cos-12cos+32sincos=-1.答案-17.(一题多空题)已知锐角,满足(tan -1)(tan -1)=2,则tan(+)=,+=.解析因为(tan-1)(tan-1)=2,所以tan+tan=tantan-1.因此tan(+)=tan+tan1-tantan=-1,因为+(0,),所以+=34.答案-1348.已知0,2,tan =2,则cos-4=.解析由tan=2,得sin=2cos.又sin2+cos2=1,0,2,cos=55,sin=255.cos-4=coscos4+sinsin4=5522+25522=31010.答案310109.tan 23+tan 37+3tan 23tan 37的值是.解析tan60=3=tan23+tan371-tan23tan37,tan23+tan37=3-3tan23tan37,tan23+tan37+3tan23tan37=3.答案310.化简求值:(1)sin(+)cos(-)+cos(+)sin(-);(2)cos(70+)sin(170-)-sin(70+)cos(10+);(3)cos 21cos 24+sin 159sin 204.解(1)原式=sin(+-)=sin2.(2)原式=cos(70+)sin(10+)-sin(70+)cos(10+)=sin(10+)-(70+)=sin(-60)=-32.(3)原式=cos21cos24+sin(180-21)sin(180+24)=cos21cos24-sin21sin24=cos(21+24)=cos45=22.11.已知,均为锐角,且tan =cos-sincos+sin,求tan(+)的值.解tan=cos-sincos+sin=1-tan1+tan=tan4-,因为,均为锐角,所以-44-4,02,又y=tanx在-2,2上是单调函数,所以=4-,即+=4,tan(+)=1.能力提升1.已知2,32,tan-4=-3,则sin =()A.55B.-55C.255D.55解析tan=tan-4+4=tan-4+tan41-tan-4tan4=-12,因为2,32,所以2,故sin=15=55.答案A2.设,都为锐角,且cos =55,sin(+)=35,则sin 等于()A.2525B.11525C.55D.-55或11525解析为锐角,cos=55,sin=255.,都为锐角,0+.sin(+)=35,cos(+)=45.当cos(+)=-45时,sin=sin(+)-=sin(+)cos-cos(+)sin=3555+45255=11525;当cos(+)=45时,sin=sin(+)-=sin(+)cos-cos(+)sin=3555-45255=-55,与已知为锐角矛盾.sin=11525.答案B3.已知cos(+)=45,cos(-)=-45,则cos cos =.解析由已知得coscos-sinsin=45,coscos+sinsin=-45,两式相加得2coscos=0,故coscos=0.答案04.已知