If `alpha, beta` are the roots of the equation `x^2 + (sin phi -1)x-1/2 cos^2 phi = 0 (phi in R),` then the maximum value of the sum of the squares of the roots is.

IF the sum of the squares of the roots of the equation x^2 - ( sin alpha - 2)x-(1 + sin alpha ) = 0 is least , then alpha =

If sin phi and cos phi are the roots of the equation ax^(2)+bx+c=0, then

Find the maximum and minimum value of the sum of the squares of the roots of the equatiorn x^(2)+(3sin phi-4)x+(1)/(2)cos^(2)phi=0. For what value of phi in (-pi,pi) these extreme values occur.

The equation whose roots are nth power of the roots of the equation,x^(2)-2x cos phi+1=0 is given by

If alpha and beta are the roots of the quadratic equation 4x ^(2) + 2x -1=0 then the value of sum _(r =1) ^(oo) (a ^(r ) + beta ^(r )) is :

If alpha and beta are the roots of the quadratic equation 4x ^(2) + 2x -1=0 then the value of sum _(r =1) ^(oo) (a ^(r ) + beta ^(r )) is :

Prove: (sin phi - cos phi) ^(2) =1 - sin 2 phi.

If sin theta sin phi - cos theta cos phi+1 =0 then the value of 1+ cot theta tan phi is-

(sec phi-tan phi)^2 (1+sin phi)^2 div sin^2 phi =?