Answer :

Let

…(i)


We know that,



So, if



[, sin (π – x) = sin x]


…(ii)


Adding these two I’s from equations (i) and (ii), we get




Solving further,





Now, we can easily integrate the Right Hand Side (RHS) of the equation.


Let us divide the numerator and denominator by cos x.




…(iii)


Now,


Let t = sec x + tan x.


Differentiating both sides with respect to x, we get




Again put t in place of tan x + sec x.



dt = t.sec x dx



Putting sec x + tan x = t and in equation (iii), we get








Substituting t = sec x + tan x, we get



Putting the upper and lower limits,







I = π



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