cot 9x

If I_(n)=int tan^(n)xdx then I_(0)+I_(1)+2(I_(2)+......+I_(8))+I_(9)+I_(10)= (a) (tan x)/(1)+(tan^(2)x)/(2)+....+(tan^(9)x)/(9), (b) -((tan x)/(1)+(tan^(2)x)/(2)+......+(tan^(9)x)/(9)) (c) (cot x)/(1)+(cot^(2)x)/(2)+......+(cot^(9)x)/(9) (d) -((cot x)/(1)+(cot^(2)x)/(2)+......+(cot^(9)x)/(9))

Minimum value of 4 tan x + 9 cot x is

Evaluate int((cos ec^(2)x)dx)/((cos ecx+cot x)^((9)/(2)))

If int(cosec^(2)x)/((cosec x+cot x)^(9/2))dx =(cosec x-cot x)^(7/2)((1)/(alpha)+((cosec x-cot x)^(2))/(11))+C (where C is constant of integration and a in N ),then a is -

If int (cosec^(2)x)/((cosec x + cot x)^(9/2)) dx = (cosec x - cot x)^(7/2)(1/alpha+((cosec x-cotx)^(2))/11)+C where C is constant of integration and alpha in N) then alpha is

(i) 4 cot x - 1/2 cos x + 2/cosx - 3/sin x + ( 6 cot x)/(cosecx) + 9 (ii) -5 tan x + 4 tan x cos x -3 cotx sec x + 2 sec x -13

Prove that tan 9 ^(@) - tan 27 ^(@)- cot 27 ^(@) + cot 9^(@)=4

Prove that : cot x cot2x+cot2x cot3x+2=cot x(cot x-cot3x)