[" ALLUSTRATIVE EXAMPLES "],[" Example 1.Show that sin x(1+cos x ) " is maximum when " x = pi / 3"]

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Show that sin x (1 + cos x), x in |0, pi| is maximum value at x = (pi)/(3) .

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Show that f(x)=sin x(1+cos x) is maximum at x=(pi)/(3) in the interval [0,pi] .

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Examples: (1)/(sin x+sqrt(3)cos x)dx