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Question

Prove that I=π20secxcosec x+secxdx=π4

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Solution

Let I=π20secxcosec xsecxdx ....(i)

I=π20sec(π2x)cosec (π2x)sec(π2x)

I=π20cosec xsecx+cosec xdx....(ii)

On adding Eqs. (i) and (ii),we get
2I=π20dx=[x]π20

I=π4

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