Question Number 104122 by Dwaipayan Shikari last updated on 19/Jul/20

(1/(sin2x))+(1/(sin2^2 x))+.....+(1/(sin2^n x))  Find the value

Answered by OlafThorendsen last updated on 19/Jul/20

(1/(sinu)) = ((sin(u−(u/2)))/(sinusin(u/2)))  (1/(sinu)) = ((sinucos(u/2)−sin(u/2)cosu)/(sinusin(u/2)))  (1/(sinu)) = ((cos(u/2))/(sin(u/2)))−((cosu)/(sinu))  (1/(sinu)) = cot(u/2)−cotu  u = 2^k x  (1/(sin2^k x)) = cot2^(k−1) x−cot2^k x  Σ_(k=1) ^n (1/(sin2^k x)) = Σ_(k=1) ^n cot2^(k−1) x−cot2^k x  = cotx−cot2x  +cot2x−cot4x  +...  +cot2^(n−1) x−cos2^n x  Σ_(k=1) ^n (1/(sin2^k x)) = cotx−cot2^n x

Commented byDwaipayan Shikari last updated on 19/Jul/20

Great sir!