Hint:Seems to be hard,but it isn't^^



  • If xk]0,π2[x_k\in\left ]0,\frac{\pi}{2}\right [,then
    (k=1nsin(xk)cos2(xk))(k=1ncos(xk)sin2(xk))274(k=1nsin2(xk))(k=1ncos2(xk))\left(\sum_{k=1}^{n}\frac{\sin(x_k)}{\cos^2(x_k)} \right)\left(\sum_{k=1}^{n}\frac{\cos(x_k)}{\sin^2(x_k)}\right)\ge\frac{27}{4}\left(\sum_{k=1}^{n}\sin^2(x_k)\right)\left(\sum_{k=1}^{n}\cos^2(x_k)\right)


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