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sec^(-1)|(1)/(4) sum(k=0)^(10) (sec((7pi...

`sec^(-1)|(1)/(4) sum_(k=0)^(10) (sec((7pi)/(12)+(kpi)/(2))sec((7pi)/(12)+(k+1)((pi)/(2)))]` will be

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Evaluate `sec^(-1)[(1)/(4)underset(k=0)overset(10)sumsec((7pi)/(12)+(kpi)/(12))sec((7pi)/(12)+(k+1)((pi)/(2)))]`
`=sec^(-1)[-(1)/(4)underset(k=0)overset(10)sum(2)/(sin((7pi)/(6)+kpi))]=sec^(-1)[-(1)/(2)underset(k=0)overset(10)sum(1)/((1-)^(k+1)sin((pi)/(6)))]=sec^(-1)(-underset(k=0)overset(10)sum(1)/((-1)^(k+1)))=sec^(-1)(1)=0`
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