Prove that : `sum_(r=1)^n tanr alpha* tan(r+1) alpha = cot alpha*tan(n+1) alpha -n -1`

Prove that: tan alpha+2tan2 alpha+4tan4 alpha+8cot8 alpha=cot alpha

Prove that (tan alpha+tan beta)/(cot alpha+cot beta)=tan alpha tan beta

(1)/(tan3 alpha-tan alpha)-(1)/(cot3 alpha-cot alpha)=cot2 alpha

Prove that tan alpha + 2tan 2alpha + 4tan 4alpha + 8cot 8alpha = cot alpha .

If 4nalpha = pi then the numerical value tan alpha* tan 2alpha *tan 3alpha ...... tan(2n -1)alpha = _____

If cot alpha+tan alpha=m and (1)/(cos alpha)-cos alpha=n, then

prove that :tan(alpha)+2tan(2 alpha)+4(tan4 alpha)+8cot(8 alpha)=cot(alpha)

Prove that: tan alpha +2tan 2alpha+ 2^(2)tan 2^(2)alpha +..... + 2^(n-1) tan 2^(n-1)alpha + 2^n cot 2^n alpha=cotalpha .