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If sin^2theta1+sin^2theta2+...+sin^2thet...

If `sin^2theta_1+sin^2theta_2+...+sin^2theta_n=0`, then find the minimum value of `costheta_1+costheta_2+...+costheta_n`.

Text Solution

Verified by Experts

The correct Answer is:
`-n`
`sin^2theta_1+sin^2theta_2+...+sin^2theta_n=0`
`rArr sintheta_1=sintheta_2=...sintheta_n=0`
`rArr costheta_1,costheta_2...,costheta_n=pm1`
Therefore, the minimum value of `costheta_1+costheta_2+…+costheta_n`
`=(-1)+(-1)+(-1)+…n" times "=-n`
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