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Prove that sinx.sin2x.sin3x <9/16

manoj jangra , 14 Years ago
Grade 12
anser 1 Answers
Sumit Majumdar

Last Activity: 10 Years ago

Dear student,
We have:
sin\left ( x \right )sin\left ( 2x \right )sin\left ( 3x \right )=2sin^{2}\left ( x \right )cos\left ( x \right )\left ( 3sin\left ( x \right ) \right-4sin^{3}\left ( x \right ) )=6sin^{3}\left ( x \right )cos\left ( x \right )-8sin^{5}\left ( x \right )cos\left ( x \right )On maximising this, we get the maximum value of sin(x) as equal to:
sin\left ( x \right )=\sqrt{\frac{8\pm \sqrt{10}}{12}}
This gives the required result.
Thanks & Regards
Sumit Majumdar,
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Ph.D,IIT Delhi

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