This is related to my previous https://www.physicsforums.com/showthread.php?t=398964". I am having trouble to get the maximum of the following trigonometric function:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\cos^m\theta_1(c\cos^n\theta_2+s\sin^n\theta_2)+\sin^m\theta_1 ( c\sin^n\theta_2+s\cos^n\theta_2)

[/tex]

Here [tex]m,n\ge2 \mbox{ are fixed positive integers and } c,s[/tex] are fixed positive reals with [tex]c^2+s^2=1[/tex]. The maximum is to be carried out w.r.t. [tex]\theta_1,\theta_2[/tex] in the range [tex]0\le\theta_1,\theta_2\le\frac{\pi}{2}[/tex] In my trying, I got the maximum to be max(c,s), but I fear may be I have done some mistake. I got the result by differentiating w.r.t. [tex]\theta_1,\theta_2[/tex] and vanishing them....but I have ignored the case when [tex]\cos\theta_1\cos\theta_2\sin\theta_1\sin\theta_2\ne0[/tex]. Can anybody help me, please.

Can I say that the function is all time differentiable within its closed and compact domain (the rectangle), the maximum should be attained on boundary?

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# Maximum of a trigonometric function

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