If `I_n` = `int_0^(pi/2) (sin^2 nx)/(sin^2 x) dx`, then

int_0^(pi/2) sin x dx

If a _(n) = int_(0) ^( (pi)/(2)) (sin^(2) nx)/( sin x) dx then a _(2) -a _(1) , a _(3) - a_(2) , a_(4) -a _(3),....... are in

If I _(n)=int _(0)^(pi) (sin (2nx))/(sin 2x)dx, then the value of I _( n +(1)/(2)) is equal to (n in I) :

int_(0)^( pi/2)(sin x)*dx