Let `theta in R and sum_(k=2)^oo sin(2^k theta)=a.` Find the value `sum_(k=0)^oo[cot^3(2^ktheta)-cot(2^ktheta)]sin^4(2^ktheta)` in terms of 'a'

Let theta in R and sum_(k=2)^(oo)sin(2^(k)theta)=a. Find the value sum_(k=0)^(oo)[cot^(3)(2^(k)theta)-cot(2^(k)theta)]sin^(4)(2^(k)theta) in terms of 'a'

If int_(0)^((pi)/(2))log sin theta d(theta)=k, then find the value of int_(0)^((pi)/(2))((theta)/(sin theta))^(2)d(theta) in terms of k

If sin 2 theta=k then the value of (tan^(3) theta)/(1+tan^(2) theta)+(cot^(3) theta)/(1+cot^(2) theta)=

If 4sin^(2)theta-3=0andtheta is acute then what is the value of (cot^(2)theta+tan^(2)theta) ?

If x= sum_(n=0)^(oo) cos ^(2n)theta , y = sum _(n=o) ^(oo) sin ^(2n)theta, z= sum _(n=0)^(oo) cos ^(2n)theta.sin ^(2n)theta and 0 lt theta lt (pi)/(2) then-

If sum_(n=0)^oo2cot^(-1) ((n^2+n-4)/2)=kpi then find the value of k

Let (3pi)/4 < theta < pi and sqrt(2 cot theta+1/sin^2 theta) = k - cot theta then k=