cos^(2)(x)/(2)

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

Evaluate: (lim)_(x rarr0)(8)/(x^(8)){1-cos((x^(2))/(2))-cos((x^(2))/(4))+cos((x^(2))/(2))cos((x^(2))/(4))}

Evaluate lim_(xto0) (8)/(x^(8)){1-"cos"(x^(2))/(2)-"cos"(x^(2))/(4)+"cos"(x^(2))/(2)"cos"(x^(2))/(4)}.

Evaluate lim_(xto0) (8)/(x^(8)){1-"cos"(x^(2))/(2)-"cos"(x^(2))/(4)+"cos"(x^(2))/(2)"cos"(x^(2))/(4)}.

If cos2x+2cos x=1 then (2-cos^(2)x)sin^(2)x is equal to

sin x = 2 ^ (n) * cos (x) / (2) * cos (x) / (2 ^ (2)) * cos (x) / (2 ^ (3)) * ... * cos ( x) / (2 ^ (n)) * sin (x) / (2 ^ (n))

Prove that sin x=2^(10) sin((x)/(2^(10))) cos (x/2) cos (x/2^(2))......cos((x)/(2^(10))) .

If lim_(x rarr 0)((1-cos((x^2)/2)-cos((x^2)/4)+cos((x^2)/2)cos((x^2)/4))/(x^8))=2^(-k) . Find k.

Evaluate: lim_(x->0)8/(x^8){1-cos((x^2)/2)-cos((x^2)/4)+cos((x^2)/2)cos((x^2)/4)}