已知向量m=(2cosx/2,1),n=(sinx/2,1)(x∈R).设函数f(x)=mn-1(1)求函数f(x)的值域(2)已知锐角△ABC的三个内角分别为A,B,C,若f(A)=5/13,f(B)=3/5,求f(C)的值
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![已知向量m=(2cosx/2,1),n=(sinx/2,1)(x∈R).设函数f(x)=mn-1(1)求函数f(x)的值域(2)已知锐角△ABC的三个内角分别为A,B,C,若f(A)=5/13,f(B)=3/5,求f(C)的值](/uploads/image/z/1627507-19-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fm%3D%282cosx%2F2%2C1%29%2Cn%3D%28sinx%2F2%2C1%29%28x%E2%88%88R%29.%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dmn-1%281%29%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E5%80%BC%E5%9F%9F%282%29%E5%B7%B2%E7%9F%A5%E9%94%90%E8%A7%92%E2%96%B3ABC%E7%9A%84%E4%B8%89%E4%B8%AA%E5%86%85%E8%A7%92%E5%88%86%E5%88%AB%E4%B8%BAA%2CB%2CC%2C%E8%8B%A5f%28A%29%3D5%2F13%2Cf%28B%29%3D3%2F5%2C%E6%B1%82f%28C%29%E7%9A%84%E5%80%BC)
已知向量m=(2cosx/2,1),n=(sinx/2,1)(x∈R).设函数f(x)=mn-1(1)求函数f(x)的值域(2)已知锐角△ABC的三个内角分别为A,B,C,若f(A)=5/13,f(B)=3/5,求f(C)的值
已知向量m=(2cosx/2,1),n=(sinx/2,1)(x∈R).设函数f(x)=mn-1
(1)求函数f(x)的值域
(2)已知锐角△ABC的三个内角分别为A,B,C,若f(A)=5/13,f(B)=3/5,求f(C)的值
已知向量m=(2cosx/2,1),n=(sinx/2,1)(x∈R).设函数f(x)=mn-1(1)求函数f(x)的值域(2)已知锐角△ABC的三个内角分别为A,B,C,若f(A)=5/13,f(B)=3/5,求f(C)的值
f(x)
=m.n-1
=(2cos(x/2),1).(sin(x/2),1)-1
=2cos(x/2)(sin(x/2)+1-1
=sinx
-1cosB=4/5
f(C)
=sinC
= sin(A+B)
= sinAcosB+cosAsinB
=(5/13)(4/5)+(12/13)(3/5)
=56/65