If xi - 0 for 1- i- n and x1-x2-xn- then the greatest value of the sum sin x1-sin x2-sin xn is equal to

The correct option is D n sin(πn) x_1+x_2+..x_n=π #10;is greatest when #10; x_1=x_2=..x_n=X . #10;Hence #10; π=nX #10;Or #160; ...

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Standard XII

Mathematics

Standard Limits to Remove Indeterminate Form

If xi > 0 f...

Question

If $x_{i} > 0$ for $1 \leq i \leq n$ and $x_{1} + x_{2} + . . . . + x_{n} = π$ then the greatest value of the sum $sin x_{1} + sin x_{2} + . . . + sin x_{n}$ is equal to

n

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0

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n sin (\frac{π}{n})

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π

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Solution

The correct option is D $n sin (\frac{π}{n})$
$x_{1} + x_{2} + . . x_{n} = π$ is greatest when
$x_{1} = x_{2} = . . x_{n} = X$ .
Hence
$π = n X$
Or
$x = \frac{π}{n}$
Hence greatest value of $sin (x_{1}) + sin (x_{2}) + . . . sin (x_{n})$
$= n sin (X)$

$= n sin (\frac{π}{n})$ .

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Similar questions

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x_{i} > 0

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x_{1} + x_{2} + . . . . . + x_{n} = π

then find the greatest value of the sum

sin x_{1} + sin x_{2} + . . . . . + sin x_{n}

Q. If

x_{i} > 0

, for

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, and

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sin x_{i} + sin x_{2} + . . . . . + sin x_{n} = . . . . . . . . .

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for

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If xi>0 for 1≤i≤n and x1+x2+....+xn=π then the greatest value of the sum sinx1+sinx2+...+sinxn is equal to

The correct option is D nsin(πn)x1+x2+..xn=π is greatest when x1=x2=..xn=X. Hence π=nX Or x=πn Hence greatest value of sin(x1)+sin(x2)+...sin(xn) =nsin(X) =nsin(πn).

If $x_{i} > 0$ for $1 \leq i \leq n$ and $x_{1} + x_{2} + . . . . + x_{n} = π$ then the greatest value of the sum $sin x_{1} + sin x_{2} + . . . + sin x_{n}$ is equal to

The correct option is D $n sin (\frac{π}{n})$
$x_{1} + x_{2} + . . x_{n} = π$ is greatest when
$x_{1} = x_{2} = . . x_{n} = X$ .
Hence
$π = n X$
Or
$x = \frac{π}{n}$
Hence greatest value of $sin (x_{1}) + sin (x_{2}) + . . . sin (x_{n})$
$= n sin (X)$

$= n sin (\frac{π}{n})$ .