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

Prove that cos(alpha-beta)/(cos alpha sin beta)=tan alpha+cot beta

(tan alpha + tan beta )/( tan (alpha + beta ))+(tan alpha - tan beta )/(tan (alpha - beta )) =

tan alpha=cot beta=a, find (alpha+beta)

The expression (tan alpha+tan beta)cot(alpha+beta)+(tan alpha-tan beta)cot(alpha-beta) is independent of both alpha and beta.

If 2tan alpha=3tan beta then tan(alpha-beta)=

If alpha + beta + gamma + delta = 2pi then prove that sum tan alpha = tan alpha *tan beta* tan gamma* tan delta *sum cot alpha .

(sec alpha * sec beta + tan alpha tan beta )^(2)-( sec alpha * tan beta + tan alpha * sec beta )^(2) =

Prove the following identities: sec(alpha + beta) = (sec alpha sec beta)/(1 - tan alpha tan beta)

Simplify be reducing to a single term : (tan alpha - tan ( alpha - beta))/(1 + tan alpha tan ( alpha - beta))