1.

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

Answer»

`a=(PI)/(8)`
`(pi)/(6)leblt(pi)/(4)`
`0ltale(pi)/(6)`
`B=(pi)/(3)`

SOLUTION :`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).,):}`


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