If `S_(1)=alpha^(2)+beta^(2)-a^(2)`, then angle between the tangents from `(alpha, beta)` to the circle `x^(2)+y^(2)=a^(2)`, is

Tangents drawn from the point (c, d) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 make angles alpha and beta with the x-axis. If tan alpha tan beta=1 , then find the value of c^(2)-d^(2) .

If alpha ne beta" but "alpha^(2)=5 alpha-3" and "beta^(2)= 5 beta-3 then the equation whose roots are (alpha)/(beta)" and "(beta)/(alpha) is

If 2 sin 2alpha=tan beta,alpha,beta, in((pi)/(2),pi) , then the value of alpha+beta is

If alpha and beta are the roots of x^(2)+6x-4=0 , find the values of (alpha-beta)^(2) .

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

If alpha" and "beta are the roots of x^(2)-ax+b^(2)=0 , then alpha^(2)+beta^(2) is equal to

If alpha and beta are the roots of x^(2)+6x-4=0 , find the value of (alpha-beta)^(2) .

Find the value of x such that ((x+alpha)^2-(x+beta)^2)/(alpha+beta)=(sin (2theta))/(sin^2 theta) , where alpha and beta are the roots of the equation t^2-2t+2=0 .

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