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已知角a的终边经过点p( 2 ,-3) 求〔sin(a+π/4)+cos(a+π/4)/cos(a+π/4)-sin(a

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已知角a的终边经过点p( 2 ,-3) 求〔sin(a+π/4)+cos(a+π/4)/cos(a+π/4)-sin(a+π/4)〕
已知角a的终边经过点p( 2 ,-3) 求〔sin(a+π/4)+cos(a+π/4)/cos(a+π/4)-sin(a
正在做啊 再答: 角a的终边过点P(2,-3),则有OP=根号(4+9)=根号13

故有sina=y/OP=-3/根号13,cosa=x/OP=2/ 根号13
原式=(sin(a+Pai/4)+cos(a+Pai/4))/(cos(a+Pai/4)-sin(a+Pai/4))
=(sin(a+Pai/4)+cos(a+Pai/4))^2/[cos^2(a+Pai/4)-sin^2(a+Pai/4)]
=[1+2sin(a+Pai/4)cos(a+Pai/4)]/cos(2a+Pai/2)
=[1+sin(2a+Pai/2)]/(-sin2a)
=[1+cos2a]/(-sin2a)
=2cos^2a/(-2sinacosa)
=-cosa/sina
=-2/(-3)
=2/3