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.
![若 cos2a/sin(a-π/4)= -√2/2,求cosa+sina的值.](/uploads/image/z/3534073-25-3.jpg?t=%E8%8B%A5+cos2a%2Fsin%EF%BC%88a-%CF%80%2F4%29%3D+-%E2%88%9A2%2F2%2C%E6%B1%82cosa%2Bsina%E7%9A%84%E5%80%BC.)
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.
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.
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