Evaluate : `lim_(n to oo) (cos(x/2)cos(x/2^2)cos(x/2^3)....cos(x/2^n))`

Evaluate ("lim")_(n→oo){cos(x/2)cos(x/4)cos(x/8)... cos(x/(2^n))}

Evaluate lim_(ntooo) {cos((x)/(2))cos((x)/(4))cos((x)/(8))...cos((x)/(2^(n)))} .

Evaluate lim_(ntooo) {cos((x)/(2))cos((x)/(4))cos((x)/(8))...cos((x)/(2^(n)))} .

Evaluate lim_(n rarr oo){cos((x)/(2))cos((x)/(4))cos((x)/(8))...cos((x)/(2^(n)))}

We have f (x) lim_(n to oo) cos (x)/(2) cos (x)/(2^(2)) cos (x)/(2^(3)) cos (x)/(2^(4)) …… …. cos (x)/(2^(n)) = ("sin" x)/(2^(n) "sin" (x)/(2^(n))) using the identity lim_(n to oo) lim_(x to 0) f(x) equals

We have f (x) lim_(n to oo) cos (x)/(2) cos (x)/(2^(2)) cos (x)/(2^(3)) cos (x)/(2^(4)) …… …. cos (x)/(2^(n)) = ("sin" x)/(2^(n) "sin" (x)/(2^(n))) using the identity lim_(n to oo) lim_(x to 0) f(x) equals

Evaluate ("lim")_(nvecoo){cos(x/2)cos(x/4)cos(x/8) cos(x/(2^n))}