Prove that `int(g(sinx))/(g(sinx)+g(cosx))dx = int_(0)^(pi/2)(g(cosx))/(g(sinx)+g(cosx))dx = (pi)/(4)`.

Prove that `int(g(sinx))/(g(sinx)+g(cosx))dx = int_(0)^(pi/2)(g(cosx))

1.	Prove that `int(g(sinx))/(g(sinx)+g(cosx))dx = int_(0)^(pi/2)(g(cosx))/(g(sinx)+g(cosx))dx = (pi)/(4)`.
Answer» Let `=overset(pi/2)underset(0)int(g(sinx))/(g(sinx)+g(cosx))dx rArr I = underset(0)overset(pi/2)int(g(sin(pi/2-x)))/(g(sin(pi/2-x))+g(cos(pi/2-x)))dx` `=overset(pi/2)underset(0)int(g(cosx))/(g(cosx)+g(sinx))dx` on adding, we obtain ` = 2I = overset(pi/2)underset(0)int((g(sinx))/(g(sinx)+g(cosx))+(g(cosx))/(g(cosx)+g(sinx)))dx =overset(pi/2)underset(0)int dx rArr I = (pi)/(4)`.

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`lim_(nrarroo) sum_(r=0)^(n-1) (1)/(sqrt(n^(2)-r^(2)))`
`lim_(nrarroo) (((n+1)(n+2)"........"3n)/(n^(2n)))^(1//n)` is equal to :A. `(27)/(e^(2))`B. `(9)/(e^(2))`C. `3 log3-2`D. `(18)/(e^(4))`