If `sin(120^(@)-alpha)=sin(120^(@)-beta),0ltalpha,betaltpi` ,then
find the relation between `alphaandbeta` .

|(alpha,-beta,0),(0,alpha,beta),(beta,0,alpha)|=0 , then

If alpha, beta, gamma are the roots of ax^(3) + bx^(2) + cx + d = 0 and |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)| = 0, alpha != beta != gamma , then find the equation whose roots are alpha + beta - gamma, beta + gamma - alpha and gamma + alpha - beta

If |(sin^(2)alpha,cos^(2)alpha),(cos^(2)alpha,sin^(2)alpha)|=0,alphain(0,pi) , then the values of alpha are

If alpha and beta are the roots of the equation x ^(2) + alpha x + beta = 0, then

If (cos^4 alpha)/(cos^2beta)+(sin^4alpha)/(sin^2beta)=1 ,then prove that sin^4alpha+sin^4beta=2sin^2alphasin^2beta .

If cos^(2)alpha-sin^(2)alpha=tan^(2)beta , then prove thta tan^(2)alpha=cos^(2)beta-sin^(2)beta .

If sinalpha=15/17 , cosbeta=12/13 and alpha and beta are in the first quadrant , find the values of sin(alpha+beta) , cos(alpha+beta) , and tan(alpha+beta)