已知COS(π/4-α)=3/5,-3/2<α<-π/2,求COS(2X-π/4)=?
热心网友
由于,-3/2π<α<-π/2则3/4π〈π/4-α〈7/4π，又因为COS(π/4-α)=3/5 〉0，则=〉3/2π〈4/7π/4-α〈7/4π 。故SIN(π/4-α)〈0 。SIN(π/4-α)=-4/5则SIN(π/2-2α）=2SIN(π/4-α)COS(π/4-α)=-12/25又因为SIN(π/2-2α）=COS2α=-12/25。。。。。。。。。。。。。。〈1式〉同理SIN2α=COS(π/2-2α）=2COS(π/4-α)的平方-1=-7/25故COS(2α-π/4)=COS2αCOSπ/4+SIN2αSINπ/4=-19乘以根号2/50PS我式心算得到的答案，可能有误，你再验算哈，方法应该是对的！