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I have the problem $$ 3^{\sin x} \cdot 3^{\sin 2x} \cdot 3^{\sin 3x} \cdot \ldots = 3. $$

I’ve converted it to $$ \sin x + \sin 2x + \sin 3x + \ldots = 1, $$ but what should I do next?

Bilbottom
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優奈高橋
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  • Welcome to Math.SE. Please write your questions using MathJax. I have edited your question this time, as questions will be better received with the right formatting. It's also great that you've shown at least one step. – Bilbottom May 13 '18 at 10:39
  • It might be helpful for you to view this post and see if you can answer your question then. – Bilbottom May 13 '18 at 10:44

1 Answers1

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Hint: Use that for your sum is hold: $$\sum_{i=1}^{n}\sin(ix)=\csc \left(\frac{x}{2}\right) \sin \left(\frac{n x}{2}\right) \sin \left(\frac{1}{2} (n+1) x\right)$$

Dr. Sonnhard Graubner
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