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Question

π0tanxsecx+cosxdx=
  1. π4
  2. π2
  3. \N
  4. π


Solution

The correct option is B π2
π0tanxsecx+cosxdx
=π0sinxcosx1cosx+cosxdx=π0sinx1+cos2xdx
Put cos x = t
Then - sin x dx = dt
x=0t=cos0=1
x=πt=cosπ=1

π0sinx1+cos2xdx
=11 11+t2(dt)
=1111+t2dt
=[tan1(t)]11
=tan1(1)tan1(1)
=tan11+tan11
=2 tan1(1)
=2.π4
=π2
 

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