82问答网 > 已知：tan（派⼀4＋a）＝1⼀2，求tana与2sinacosa－cos平方a⼀2cos平方a＋sin平方a的值

已知：tan（派⼀4＋a）＝1⼀2，求tana与2sinacosa－cos平方a⼀2cos平方a＋sin平方a的值

急需，详细步骤
2025-03-25 19:42:38
推荐回答（1个）
回答1：

tan（派/4＋a）＝1/2,
tana=tan[(派/4＋a)-派/4]＝[tan(派/4＋a)-tan(派/4)]/[1+tan(派/4＋a)tan(派/4)]=(1/2-1)/[1+(1/2)*1]=-1/3,
[2sinacosa－(cosa)^2]/[2(cosa)^2＋(sina)^2]
={[2sinacosa－(cosa)^2]/[(cosa)^2]}/{[2(cosa)^2＋(sina)^2]/[(cosa)^2]}=
=(2tana－1)/[2＋(tana)^2]=[2*(-1/3)－1]/[2＋(-1/3)^2]=-15/19

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