Limits

Simplify
\prod_{n=1}^{\infty }{cos(\frac{x}{2^n})}

it comes out to be \frac{sinx}{x} but how?

7 Answers

iska ek formula hai... [3]

tumhe kya derivation chaiye us formula ka ??

waise..

given thing = cos(x/2)cos(x/4)cos(x/8).....cos(x/2^n)

= sin[2ⁿ⁺¹(x/2ⁿ)]/2ⁿ⁺¹ sin(x/2ⁿ)

abhi toh ho jaega yahan se...

put n-> infinity.

i don't think i follow :(

well there's a formula:

cosAcos2Acos4A.......cos2^n-1A = sin2ⁿA/ 2ⁿsinA

yeah i've seen that before,but couldn't remember,ok thanks i'll try that

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