If `int_0^((pi)/(2))(dx)/(1+tanx+cotx)=a` and `int_0^(pi/2)(tanx)/(1+tanx+cotx)=b` then which of the following is/are correct

Options

A. `a=(pi)/(8)`
B. `(pi)/(6)leblt(pi)/(4)`
C. `0ltale(pi)/(6)`
D. `b=(pi)/(3)`

Answer

A

Explanation

`tanx+cotge2rArr0lt(1)/(tanx+cotx)=(1)/(2)" (As"s in(0,(pi)/(2)))`
`0ltunderset(0)overset((pi)/(2))(f)(dx)/(1+tanx+cotx)leunderset(0)overset((pi)/(2))(f)(dx)/(1+2)`
`:." "0ltale(pi)/(6)`
`{:(b=underset(0)overset((pi)/(2))(f)(tanxdx)/(1+tanx+cotx),"Apply (King) ":.,2b=underset(0)overset((pi)/(2))(f)(tanx+cotx+1-1)/(1+tanx+cotx)dx,),(2b=underset(0)overset((pi)/(2))(f)dx-a,:.b=(pi)/(4)-(a)/(2),:.(pi)/(6)leblt(pi)/(4).,):}`