已知cos(a-π/4)=1/4,求sin2a的值

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已知cos(a-π/4)=1/4,求sin2a的值

cos(a-π/4) = 1/4 ,
cosa*cos(π/4)+sina*sin(π/4) = 1/4 ,
(√2/2)(cosa+sina) = 1/4 ,
(√2/2)²(cosa+sina)² = (1/4)² ,
(1/2)(cos²a+sin²a+2sinacosa) = 1/16 ,
(1/2)(1+sin2a) = 1/16 ,
1+sin2a = 1/8 ,
sin2a = -7/8 .

-7/8