Factorise `alpha^2 +beta^2 + alpha beta`

(a) show that alpha^2 + beta^2 + alpha beta =0

If alpha , beta are the roots of ax ^2 + bx +c=0 then alpha ^5 beta ^8 + alpha^8 beta ^5=

Show that cos ^2 alpha + cos^2 (alpha +Beta) - 2 cos alpha cos betacos (alpha+ beta) =sin^2 beta

alpha + beta = 5 , alpha beta= 6 .find alpha - beta

Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + cos 2(alpha + beta) = cos 2alpha

Prove that (sin alpha cos beta + cos alpha sin beta) ^(2) + (cos alpha coa beta - sin alpha sin beta) ^(2) =1.

The lengths of the sides of a triangle are alpha-beta, alpha+beta and sqrt(3alpha^2+beta^2), (alpha>beta>0) . Its largest angle is

If alpha and beta are acute such that alpha+beta and alpha-beta satisfy the equation tan^(2)theta-4tan theta+1=0 , then (alpha, beta ) =

Prove that : (cos alpha + cos beta)^2 + (sin alpha + sin beta)^2 = 4 cos^2 ((alpha-beta)/(2))

Let -pi/6 beta_1 and alpha_2 >beta_2 , then alpha_1 + beta_2 equals: