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`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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Answer» 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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