4.6两角和与差的正弦、余弦、正切(3)sinsincoscos)cos(:][)(C公式sinsincoscos)cos(:][)(C公式sincoscossin)sin(:][)(S公式sincoscossin)sin(:][)(S公式.tantan1tantan)(tan:][)(T公式.tantan1tantan)(tan:][)(T公式复习:例1.)33sin()34sin()33cos()34sin(xxxx化简解:原式)33sin()34sin()33cos()34cos(xxxx)3334cos(xx=127cos=)-(=125cos.125cos=-2)34()34(xx-125cos.A125cos.B125sin.C125sin.D故选B例2求证:sin3cos.)6sin(2证明:)6sin(2)sin6coscos6(sin2)sin23cos21(2sin3cossin3cos.)6sin(2一般地:cossinba22ba)cossin(2222babbaa22ba)cossinsin(cos22ba.)sin(.tancossin2222共同确定,,由其中abbaabab.50sin10cos310tan化简例3解:50sin10cos310cos10sin原式50sin10cos10cos10cos310sin50sin10cos2310sin21250sin)6010sin(250sin)50sin(2.280sin2)10tan31(10sin50sin22化简练习1.解:80sin210cos10sin310cos10sin50sin2原式10cos210cos10sin2310cos2110sin250sin2)1060cos(10sin10cos50sin22)1050sin(2223226例4.解:;)(求值:70sin20sin10cos2120cos20sin)2030cos(21原式)(20cos20sin)20sin30sin20cos30(cos220cos20cos3.3.6sin15sin)615cos(6sin15cos)615sin(原式.6sin15sin6sin15sin6cos15cos6sin15cos6sin15cos6cos15sin;6sin15sin9cos6sin15cos9sin)2(6cos15cos6cos15sin15tan)3045tan(30tan45tan130tan45tan.32解:tan2)tan()2sin(sin32:求证,且满足,是锐角、已知代入条件得,由:证明)()(2])sin[(])sin[(3sin)cos(cos)sin(sin)cos(3cos)sin(3即sin)cos(2cos)sin(2,为锐角、cossin2)cos()sin(tan2)tan(故例5:.)45tan1)(44tan1()2tan1)(1tan1(求值例623244tan1tan44tan1tan1)44tan1)(1tan1(解:44tan1tan)44tan1tan1(45tan12同理可得2)43tan1)(2tan1(2)44tan1)(1tan1(即2)23tan1)(22tan1()45tan1)(44tan1()2tan1)(1tan1(例7.解:.cos31sinsin21coscos)(,求,已知,等式两端平方,想到31sinsin21coscossinsincoscos)cos(由)(得141coscos2coscos22)(291sinsin2sinsin22得)()(由213613cos22)(即9141sinsincoscos22.7259cos)(练习2..sin53sin31cosCBAABC求,,,中已知在解:CBAABC,中在)(即BAC)](sin[sinBAC)sin(BABABAsincoscossin31cosAA2,322cos1sin2AA53sinB又20B,54sin1cos2BB53)31(54322sinC.15328练习3.,且,是锐角,已知71cos.1411)cos(求,分析:)(注意到解:,且,是锐角71cos2co...