Q. if `f(n,theta)=prod_(r=1)^n(1-tan^2(theta/2^t))`, then compute `lim_(n->oo)f(n,theta)`

Q. if f(n,theta)=prod_(r=1)^n(1-tan^2(theta/2^r)) , then compute lim_(n->oo)f(n,theta)

if f(n,theta)=prod_(r=1)^(n) (1-tan^(2)(theta)/(2^(r))) then the value of lim_(thetato0) [lim_(ntoinfty) f(n,theta)] , (where [x] represent the greatest integer function) is

f_(n)(theta)=sum_(n=1)^(n)tan((theta)/(2^(n)))sec((theta)/(2^(n-1))), then compute the value of f_(4)((4 pi)/(3))

If f(n)=prod_(r=1)^(n)cos r,n in N , then

If f(n)=prod_(r=1)^(n)cos r,n in N , then

If f (theta)=4/3 (1- cos ^(6) theta - sin ^(6)theta), then lim _(xtoo) 1/n [sqrt(f ((1)/(n)))+sqrt(f ((2)/(n)))+sqrt(f((n)/(n)))]=

If f (theta)=4/3 (1- cos ^(6) theta - sin ^(6)theta), then lim _(ntooo) 1/n [sqrt(f ((1)/(n)))+sqrt(f ((2)/(n)))+sqrt(f((n)/(n)))]=

For theta_(1), theta_(2), ...., theta_(n) in (0, pi/2) , if ln(sec theta_(1)-tan theta_(1))+ "ln" (sec theta_(2)-tan theta_(2))+...... +"ln" (sec theta_(n)-tan theta_(n))+"ln" pi=0 , then the value of cos((sec theta_(1)+ tan theta_(1))(sec theta_(2)+tan theta_(2))....(sec theta_(n)+tan theta_(n))) is equal to

If x_(k)=(sec theta)^((1)/(2^(k)))+(tan theta)^((1)/(2^(k)))quad and y_(k)=(sec theta)^((1)/(2k))-(tan theta)^((1)/(2^(k))), then value of 3y_(n)prod_(k=0)^(n)(x_(k)) is equal to