If the points `(2,beta, 3), B(alpha,-6,1) and C(-1, 11,9)` are collinear find the values of `alpha` and `beta` by vector method

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

If sin alpha.sinbeta - cos alpha.cos beta+1=0 , then find the value of cot alpha.tan beta .

If sin alpha sin beta - cos alpha cos beta + 1=0, then the value of 1+cot alpha tan beta is

If alpha and beta are zeroes of 8x^(2)-6x+1 , then find the value of (1)/(alpha)+(1)/(beta) .

If alpha, beta and 1 are the roots of x^3-2x^2-5x+6=0 , then find alpha and beta

If alpha and beta are zeroes of 5x^(2)-7x+1 , then find the value of (1)/(alpha)+(1)/(beta) .

If alpha and beta are zeroes of the polynomial 3x^(2)+6x+1 , then find the value of alpha+beta+alpha beta .

If sin(alpha+beta)=1 and sin(alpha-beta)=1/2 , where 0lt=alpha, betalt= pi/2 , then find the values of tan(alpha+2beta) and tan(2alpha+beta) .

If alpha and beta (alpha gt beta) are the roots of x^(2) + kx - 1 =0 , then find the value of tan^(-1) alpha - tan^(-1) beta

If alpha,beta are roots of x^2-3x+a=0 , a in R and alpha <1< beta then find the value of a.