已知tana=2,求cos^4((π/3)+a)-cos^4((a-π)/6)的值已知tana=2,求cos^4((π/3)+a)-cos^4(a-(π/6))的值 原题不对 是这题
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![已知tana=2,求cos^4((π/3)+a)-cos^4((a-π)/6)的值已知tana=2,求cos^4((π/3)+a)-cos^4(a-(π/6))的值 原题不对 是这题](/uploads/image/z/5169753-9-3.jpg?t=%E5%B7%B2%E7%9F%A5tana%3D2%2C%E6%B1%82cos%5E4%28%28%CF%80%2F3%29%2Ba%29-cos%5E4%EF%BC%88%28a-%CF%80%29%2F6%EF%BC%89%E7%9A%84%E5%80%BC%E5%B7%B2%E7%9F%A5tana%3D2%2C%E6%B1%82cos%5E4%28%28%CF%80%2F3%29%2Ba%29-cos%5E4%EF%BC%88a-%28%CF%80%2F6%29%EF%BC%89%E7%9A%84%E5%80%BC+%E5%8E%9F%E9%A2%98%E4%B8%8D%E5%AF%B9+%E6%98%AF%E8%BF%99%E9%A2%98)
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已知tana=2,求cos^4((π/3)+a)-cos^4((a-π)/6)的值已知tana=2,求cos^4((π/3)+a)-cos^4(a-(π/6))的值 原题不对 是这题
已知tana=2,求cos^4((π/3)+a)-cos^4((a-π)/6)的值
已知tana=2,求cos^4((π/3)+a)-cos^4(a-(π/6))的值
原题不对 是这题
已知tana=2,求cos^4((π/3)+a)-cos^4((a-π)/6)的值已知tana=2,求cos^4((π/3)+a)-cos^4(a-(π/6))的值 原题不对 是这题
cos^4((π/3)+a)-cos^4(a-(π/6))
=cos^4((π/3)+a)-cos^4((π/6)-a)
=cos^4((π/3)+a)-sin^4((π/3)+a)
=[cos^2((π/3)+a)+sin^2((π/3)+a)]*[cos^2((π/3)+a)-sin^2((π/3)+a)]
=cos^2((π/3)+a)-sin^2((π/3)+a)
=cos((2π/3)+2a)
=cos2acos(2π/3)-sin2asin(2π/3)
tana=2,cos²a=1/(1+tan²a)=1/5
cos2a=2cos²a-1= -3/5
sin2a=2sina*cosa=2sina*cosa*cos²a/cos²a=2tana*cos²a=4/5
原式=-3/5*(-1/2)-4/5*(√3/2)=(3-4√3)/10