if cos2 theta + 2 cos theta is always
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cos2 theta+2cos theta
2cos^2 theta-1+2cos theta
2(cos theta+1/2) ^2-3/2
2(cos theta+1/2) ^2>or equal to 0 for all theta
2(cos theta+1/2) ^2-3/2>or equal to -3/2 for all theta
cos2 theta+2cos theta>or equal to -3/2 for all theta
Maximum value of this expression is 3
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