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If x1, a n dx2 are the roots of x^2+(sin...

If `x_1, a n dx_2` are the roots of `x^2+(sintheta-1)x-1/(2cos^2theta)=0,` then find the maximum value of `x1 2+x2 2dot`

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Verified by Experts

The correct Answer is:
4
`x_(1)+x_(2) = ( 1 - sin theta), x_(1)+x_(2) = - (1)/(2) cos^(2) theta`
Now, `x_(1)^(2)+x_(2)^(2) = ( x_(1)+x_(2))^(2) - 2x_(1)+x_(2)`
= ` ( - sin theta)^(2) + cos^(2) theta`
= `2 - 2 sin theta`
`rArr x_(1)^(2)+x_(2)^(2) |_(max)=2 + 2 = 4`
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