Sum the series `cosectheta+cosec 2theta+cosec 4 theta+…+n` terms

Find the sum of the series cosec theta+csc2 theta+csc4 theta+... to nterms .

Find the sum of the series cosectheta*cosec2theta+cosec2theta*cosec 3theta+cosec3theta*cosec 4theta+… to n tems

Prove that cosec 2alpha = cot alpha - cot 2alpha . Hence or otherwise prove that cosec theta + cosec 2theta + cosec 4theta + cosec 8theta = cot theta/2 - cot 8theta .

Prove that (sin theta + cos theta )( cosec theta - sec theta ) = cosec theta. Sec theta -2 tan theta

(1)/(cosec theta+cot theta)=cosec theta-cot theta

The value of 2 sec^(2) theta - sec^(4) theta - 2 cosec^(2)theta + cosec^(4) theta is

(sqrt((cosec^(2)theta-1)))/(cosec theta)=cos theta

cosec^4 theta-cot^4 theta=cosec^2theta+cot^2 theta

If cosec theta + cot theta= 2.5 , then cosec theta = ?