If `alpha, beta, gamma` be the eccentric angles of three points of an ellipse, the normals at which are concurrent, show that `sin(alpha+beta) + sin (beta+gamma) + sin (gamma + alpha) = 0`.

If alpha and beta are the eccentric angles of the extremities of a focal chord of an ellipse, then prove that the eccentricity of the ellipse is (sinalpha+sinbeta)/("sin"(alpha+beta))

cos alpha sin (beta-gamma) + cos beta sin (gamma-alpha) + cos gamma sin (alpha-beta)=

Find the area of the triangle whose vertices are : (a cos alpha, b sin alpha), (a cos beta, b sin beta), (a cos gamma, b sin gamma)

If alpha , beta , gamma are the roots of the equation x^3 +px^2 + qx +r=0 then the coefficient of x in cubic equation whose roots are alpha ( beta + gamma ) , beta ( gamma + alpha) and gamma ( alpha + beta) is

If alpha,beta,gamma are the angles of a triangle and system of equations cos(alpha-beta)x+cos(beta-gamma)y+cos(gamma-alpha)z=0 cos(alpha+beta)x+cos(beta+gamma)y+cos(gamma+alpha)z=0 sin(alpha+beta)x+sin(beta+gamma)y+sin(gamma+alpha)z=0 has non-trivial solutions, then triangle is necessarily a. equilateral b. isosceles c. right angled "" d. acute angled

If a line makes angles alpha, beta, gamma when the positive direction of coordinates axes, then write the value of sin^(2) alpha + sin^(2) beta + sin^(2) gamma .

If alpha , beta , gamma are the roots of x^3 + 2x^2 + 3x +8=0 then ( alpha + beta ) ( beta + gamma) ( gamma + alpha ) =

If alpha, beta and gamma are the roots of the equation x^(3)+x+2=0 , then the equation whose roots are (alpha- beta)(alpha-gamma), (beta-gamma)(beta-gamma) and (gamma-alpha)(gamma-alpha) is

If a line makes anles alpha, beta, gamma with the coordinate axes, porve that sin^2alpha+sin^2beta+sin^2gamma=2

Prove that: |(sinalpha, cosalpha, 1),(sinbeta, cosbeta, 1),(singamma, cosgamma, 1)|=sin(alpha-beta)+sin(beta-gamma)+sin(gamma-alpha)