MathDB

5

Part of 2004 South East Mathematical Olympiad

Problems(1)

trigonometric inequality

Source: China south east mathematical olympiad 2004 day2 problem 5

6/29/2013
For θ∈[0,π2]\theta\in[0, \dfrac{\pi}{2}], the following inequality 2(2a+3)cos⁡(θ−π4)+6sin⁡θ+cos⁡θ−2sin⁡2θ<3a+6\sqrt{2}(2a+3)\cos(\theta-\dfrac{\pi}{4})+\dfrac{6}{\sin\theta+\cos\theta}-2\sin2\theta<3a+6 is always true. Determine the range of aa.
inequalitiestrigonometry