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

5 years ago

Answers : (2)

Lab Bhattacharjee
121 Points
							
\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
5 years ago
Lab Bhattacharjee
121 Points
							
\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
5 years ago
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