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Trigonometry> what is the minimum value of 3 sin 6x + 3...

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what is the minimum value of 3^{sin 6x} + 3^cos6x ??

Souhardya Mondal , 9 Years ago

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Lab Bhattacharjee

Last Activity: 9 Years ago

$\text{Using AM, GM inequality,} \\ \dfrac{3^{\cos6x}+3^{\sin6x}}2\ge \sqrt{3^{\cos6x\cdot\sin6x}} \\ \text{Now,} \cos6x\cdot\sin6x=\dfrac{\sin12x}2 \\ \text{ and} \sin12x\le1$

Lab Bhattacharjee

Last Activity: 9 Years ago

$\text{There was typo in the previous answer} \\ \text{Using AM, GM inequality } \dfrac{3^{\cos6x}+3^{\sin6x}}2\ge\sqrt{3^{\cos6x+\sin6x}} \\ \text{ Now,}\cos6x+\sin6x =\sqrt2\cos(6x-45^\circ)\le\sqrt2$

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