Ye Baat Yaad Rakhna Beta Ji

Prove that: | alpha beta gamma alpha^(2)beta^(2)gamma^(2)beta+gamma gamma+alpha alpha+beta|=(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma)

If alpha!=beta and alpha^(2)=5 alpha-3 and beta^(2)=5 beta-3. find the equation whose roots are alpha/ beta and beta/ alpha .

Name the Maratha Saint who was a contemporary of Shiva ji.

If alpha,beta are the roots of x^(2)-px+q=0 then the equation whose roots are alpha beta+alpha+beta,alpha beta-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.