数学卷17:设sin2a=1/4,且α∈(π/4,π/2),求cosα-sinα的值( )求详解,
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数学卷17:设sin2a=1/4,且α∈(π/4,π/2),求cosα-sinα的值( )求详解,
数学卷17:设sin2a=1/4,且α∈(π/4,π/2),求cosα-sinα的值( )求详解,
数学卷17:设sin2a=1/4,且α∈(π/4,π/2),求cosα-sinα的值( )求详解,
解
∵a∈(π/4,π/2)
∴sina>cosa
∴cosa-sina
(cosα-sinα)²=cos²α-2sinα*cosα+sin²α=1-sin2α=1-1/4=3/4
α∈(π/4,π/2)
cosα-sinα<0
cosα-sinα=-√3/2