If `cos(x/2) cos (x/2^2) cos (x/2^) ..... cos (x/2^n)=sinx/(sin(x/2^n)` prove that` 1/2tan(x/2)+1/4tan(x/4).....1/2^(2n)tan(x/2^n)=1/2^ncot(x/2^n)-cotx`

Find the sum: tan x + 1/2 tan x/2+ 1/2^(2) tan x/2^(2) +.....+1/2^(n-1) tan x/2^(n-1)

cos x*cos2x*cos4x......cos(2^(n-1)x)=(sin2^(n)x)/(2^(n)sin x)AA n in N

Prove the following by the principle of mathematical induction: 1/2tan(x/2)+1/4tan(x/4)+...+(1/2^n)tan(x/(2^n))=(1/2^n)cot(x/(2^n)) - cot x for all n belongs to N.

If f(x) = cos x cos 2x cos 2^2 x cos^(2^3) x .....cos 2^(n-1) x and n gt 1 then f^(1)(pi/2) is

(1)/(2) tan"" ((x)/(2) ) + (1)/( 4) (tan"" (x)/(4) ) + ...... + (1)/(2^(n) ) tan"" ((x)/( 2^n) ) =

Find the period of f(x)=sinx+tan(x/2)+sin(x/(2^2))+t a n (x/(2^3))+....+sin(x/(2^(n-1)))+tan(x/(2^n))

Prove that cos^(-1)((1-x^(2n))/(1+x^(2n)))=2 tan^(-1)x^n

Prove the following by the principle of mathematical induction: (1)/(2)tan((x)/(2))+(1)/(4)tan((x)/(4))++1/2^(n)tan((x)/(2^(n)))=(1)/(2^(n))cot((x)/(2^(n)))-cot x for all nin N backslash and backslash0