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Grade Select GradeTrigonometry

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

Profile image of Souhardya Mondal
11 Years agoGrade Select Grade
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2 Answers

Profile image of Lab Bhattacharjee
11 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
Profile image of Lab Bhattacharjee
11 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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