Question

find the maximum value of u, where
u=sin x .sin y .sin(x+y) ????​

Answer 1

Answer:

What are the maximum and minimum values of sinx siny sin(x+y)?

Calling the expression m and focussing on just one period,

∂m∂x=cosxsinysin(x+y)+sinxsinycos(x+y)=0

and

∂m∂y=sinxcosysin(x+y)+sinxsinycos(x+y)=0

from which

cosxsinysin(x+y)=sinxcosysin(x+y)⇒sin(x+y)sin(x−y)=0 .

Then x=y . From this sinx=0 or \sin 3x=0 the latter giving x=π3 giving a maximum of 33√8 .

I leave it to you to determine the minimum and track through the 2 ignored situations.

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Answer 2

Answer:

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Step-by-step explanation:

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