已知cos(a+派\4)=3\5,[派\2,3派\2],求cos(2a+派\4)的值
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![已知cos(a+派\4)=3\5,[派\2,3派\2],求cos(2a+派\4)的值](/uploads/image/z/3713911-7-1.jpg?t=%E5%B7%B2%E7%9F%A5cos%28a%2B%E6%B4%BE%5C4%29%3D3%5C5%2C%5B%E6%B4%BE%5C2%2C3%E6%B4%BE%5C2%5D%2C%E6%B1%82cos%282a%2B%E6%B4%BE%5C4%29%E7%9A%84%E5%80%BC)
已知cos(a+派\4)=3\5,[派\2,3派\2],求cos(2a+派\4)的值
已知cos(a+派\4)=3\5,[派\2,3派\2],求cos(2a+派\4)的值
已知cos(a+派\4)=3\5,[派\2,3派\2],求cos(2a+派\4)的值
cos(a+π/4)=3/5
cos(2a+π/2)=2cos^2(a+π/4)-1=-7/25
∵a∈[π/2,3π/2],∴结合上式2a∈[π,3π/2],
又sin2a=-cos(2a+π/2)=7/25
cos2a=-24/25
cos(2a+π/4)=cos2a*cos(π/4)-sin2a*sin(π/4)
=-17√2/50