课题:两角和与差的正切课题:两角和与差的正切朝花夕拾目标1目标2目标1和角与差角正切公式的推导tantantan1tantantantantan1tantan目标2和角与差角正切公式的应用tantantan1tantantantantan1tantan例题1例题3例题2基础应用例题1例题1、不查表求值1tan105()75tan2)(15tan3)(tan(6045)tan(4530)23tan(4530)23tan60tan451tan60tan4531131231221tan,tan(),tan(2).25例题、()已知求例题1例题3例题2例题2基础应用2解:tan(2)tan()tantan()1tantan()12()25121()25112442tan,tan(),tan2.55例题、(2)已知求例题1例题3例题2例题2基础应用2解:tan2tan()()tan()tan()01tan()tan()212tan,tan(),tan().5444例题、(3)已知求基础应用例题1例题3例题2例题244解:tantan44tan()tan41tan()tan4322例题3、计算例题1例题3例题2例题3基础应用1tan341tan()已知,化简1tan151tan15(1)1cot151tan75(2)1tan153tan60tan15(4)计算tan45tan151tan45tan151tan75tan4575tan1203.1tan75=()tan4,=11tan1511tan303331tan15=tantan1tantantan.1tan1tantantan4515tan603.()tantantan1tantantantantan1tantan变形应用变形公式例题1例题3例题2例题4例题5例题6例题1tantantan1tantantantantan1tantan1tan17tan433tan17tan43例题、tan17431tan17tan433tan17tan43变形公式例题1例题3例题2例题4例题5例题6tan601tan17tan433tan17tan433.变形应用tantantan1tantantantantan1tantantan3tan2tantan3tan2tan.例题2、求证:tan321tan3tan2tantan1tan3tan2tantan3tan2tan.证明:左边右边原等式成立变形公式例题1例题3例题2例题4例题5例题2例题6变形应用tantantan1tantantantantan1tantantantantantantantan.ABCABC例题3、在非直角三角形中,求证:ABC证明:由题意变形公式例题1例题3例题2例题4例题5例题3例题6tan1tantantanABABC左边tan1tantantanCABCtan1tantantanCABCtantantanABC右边.原等式成立变形应用tantantan1tantantantantan1tantantantantantantantan.ABCkABCABC例题4、已知,求证:tan1tantantantan1tantantanABABCkCABC证明:左边tan21tantantan21,()tan1tantantantan1tantantantantantannCABCknnZCABCCABCABC当时,左边右边tan21tantantan2,()tan1tantantantan1tantantantantantannCABCknnZCABCCABCABC...