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若 cos2a/sin(a-π/4)= -√2/2,求cosa+sina的值.

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若 cos2a/sin(a-π/4)= -√2/2,求cosa+sina的值.
cos2a/sin(a-π/4)= -√2/2,
sin(π/2-2a) /sin(a-π/4)= -√2/2,
-sin(2a-π/2) /sin(a-π/4)= -√2/2,
[-2 sin(a-π/4)cos(a-π/4)) /sin(a-π/4)= -√2/2,
-2 cos(a-π/4))= -√2/2,
-2[cos a cosπ/4+sin a sinπ/4] = -√2/2,
-√2(cosa+sina) = -√2/2,
所以cosa+sina=1/2.