If ${b_n} = \int_0^{{\pi \over 2}} {{{{{\cos }^2}nx} \over {\sin x}}dx,\,n \in N} $, then
${b_3} - {b_2},\,{b_4} - {b_3},\,{b_5} - {b_4}$ are in A.P. with common difference $-$2
${1 \over {{b_3} - {b_2}}},{1 \over {{b_4} - {b_3}}},{1 \over {{b_5} - {b_4}}}$ are in an A.P. with common difference 2
${b_3} - {b_2},\,{b_4} - {b_3},\,{b_5} - {b_4}$ are in a G.P.
${1 \over {{b_3} - {b_2}}},{1 \over {{b_4} - {b_3}}},{1 \over {{b_5} - {b_4}}}$ are in an A.P. with common difference $-$2
