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If thetaigt0" for "1lethetalenandtheta1+...

If `theta_igt0" for "1lethetalenandtheta_1+theta_2+theta_3+...+theta_n=pi`then the greatest value of sum `sintheta_1+sintheta_2+sintheta_3+…+sintheta_n` is equal to

A

A. n

B

B. `nsin(pi/n)`

C

C. `pi`

D

D. None of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`0ltiltpi,i=1,2,3,...n`
`:. sintheta_i?0,i=1,2,3,...n`
`"Now",((sintheta_1+sintheta_2+sintheta_3+...+sintheta_n)/n)`
`lesin.((theta_1+theta_2+theta_3+...+theta_n)/n)=sin(pi/n)`
`:. sintheta_1+sintheta_2+sintheta_3+...+sintheta_nlensin(pi/n)`
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