解方程cos2A=cosA+sinA

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解方程cos2A=cosA+sinA
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解方程cos2A=cosA+sinA
解方程cos2A=cosA+sinA

解方程cos2A=cosA+sinA
即cos²a-sin²a=cosa+sina
(cosa+sina)(cosa-sina)=cosa+sina
所以cosa+sina=0或cosa-sina=1
√2sin(x+π/4)=0,-√2sin(x-π/4)=1
x+π/4=kπ,x-π/4=2kπ-3π/4,x-π/4=2kπ-π/4
x=kπ-π/4,x=2kπ-π/2,x=2kπ