We know that,
[∵, sin (π – x) = sin x]
Adding these two I’s from equations (i) and (ii), we get
Now, we can easily integrate the Right Hand Side (RHS) of the equation.
Let us divide the numerator and denominator by cos x.
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
Rate this question :