If `A=[(1,-alpha),(alpha,beta)]` and` A A^T=I` .Then find the value of `alpha` and `beta`

If for the matrix , A = [(1,-alpha),(alpha, beta)], A A^T = I_2 , then the value of alpha^4 + beta^4 is:

If cos(alpha+beta)+sin(alpha-beta)=0 and tan beta ne1 , then find the value of tan alpha .

If alpha and beta are two positive acute angles satisfying alpha-beta=15^(@) and sin alpha=cos2 beta then find the value of alpha+beta

If alpha+beta=90^(@),alpha=2beta , then find the value of cos^(2)alpha+sin^(2)beta .

tan(alpha+beta)=(1)/(2),tan(alpha-beta)=(1)/(3), then find the value of tan2 alpha

If z^2+alphaz+beta has one root 1-2i , then find the value of alpha-beta (alpha,beta , in R)

If alpha,beta are zeros of x^(2)-3x+1=0 then find the value of (alpha^(2014)+beta^(2014)+alpha^(2016)+beta^(2016))/(alpha^(2015)+beta^(2015))

If 5tan alpha tan beta=3 , then find the value of (cos(alpha+beta))/(cos(alpha-beta))