若cos2a⼀sin((a-(π⼀4))=-(√2)⼀2 求sina-cosa

高一数学题
2025-04-13 11:34:15
推荐回答(2个)
回答1:

cos(2a) = -(√2/2)sin(a-(π/4))
(cos²a-sin²a)= -(√2/2)[sinacos(π/4)-cosasin(π/4)]
(cosa+sina)(cosa-sina)= -(√2/2)[(√2/2)sina-(√2/2)cosa]
(cosa+sina)(cosa-sina) = -(1/2)(sina-cosa)
(cosa+sina)(cosa-sina)+(1/2)(sina-cosa) = 0
(cosa+sina+1/2)(cosa-sina)=0
所以:cosa+sina = -1/2,或者cosa = sina

回答2: