[" If "| alpha|,| beta|<1,1-alpha+alpha^(2)-alpha^(3)+...oo=s_(1),1-beta+beta^(2)-beta^(3)+...oo=s_(2)" then "],[1-alpha beta+a^(2)beta^(2)-a^(3)beta^(3)+....oo" equals "]

Find the value of f(alpha, beta) =|(cos (alpha + beta), -sin (alpha + beta), cos 2beta),(sin alpha, cos alpha, sin beta),(-cos alpha, sin alpha, cos beta)|

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)

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) .

Two real numbers alpha and beta are such that alpha+beta=3 and | alpha-beta|=4 then alpha nad beta are the roots of the equation:

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

Write the quadratic equations, if (i) alpha + beta = - 10 , alpha beta = 7 (ii) alpha + beta = 4, alpha beta = - 2

Write the quadratic equations, if (i) alpha + beta = -6, alpha beta = 4 (ii) alpha + beta = 8 , alpha beta = -3

If alpha, beta, gamma are the roots of x^(3) + ax^(2) + b = 0 , then the value of |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)| , is