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Let 0lt=beta(r)lt=1 and sum(r=1)^(k)cos^...

Let `0lt=beta_(r)lt=1` and `sum_(r=1)^(k)cos^(-1)beta_(r)=(k pi)/(2)` for any `kgt=1` and `A=sum_(r=1)^(k)(beta_(r))^(r)` ,then the number of solutions of the equation `tan^(2)x-sec^(10)x+1=A in (0,A+10)` is/are (1) 3 (2)2 (3) 1 (4)zero

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