First slide
Extreme values and Periodicity of Trigonometric functions
Question

If xi>0, 1in,  and x1+x2+x3+xn=π, then the greatest value of sinx1+sinx2+sinx3+...+sinxn=

Difficult
Solution

 We have sinx1+sinx2+sinx3+.+sinxnn              sinx1+x2+x3+.+xnn    since sin is concave in 0,π                sinπn   x1+x2+x3+.+xn=πsinx1+sinx2+sinx3+.+sinxnnsinπn

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