LIMIT

jus the rough method,

concider

y=-log[cos∂ cos∂/2 cos∂/2².....cos∂/2ⁿ]...1)
=-[log(cos∂)+log(cos∂/2)+......+log(cos∂/2ⁿ)]
notice that the series u need is dy/d∂

we know y= -log[sin(∂)/{2ⁿsin(∂/2ⁿ)}]

now differentiate both sides wrt ∂ and get y lim n->∞

to get the req. answer

cheers!!

ans is : 1/x - cot x +tan x

simple application of series rules......