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)`

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

Prove that |(sin alpha,cos alpha,sin(alpha+delta)),(sin beta,cos beta,sin(beta+delta)),(sin gamma,cos gamma,sin(gamma+delta))|=0

The value of the determinant Delta = |(cos (alpha + beta),- sin (alpha + beta),cos 2 beta),(sin alpha,cos alpha,sin beta),(- cos alpha,sin alpha,- cos beta)| , is

The value of the determinant Delta = |(sin 2 alpha,sin (alpha + beta),sin (alpha + gamma)),(sin (beta + gamma),sin 2 beta,sin (gamma + beta)),((sin gamma + alpha),sin (gamma + beta),sin 2 gamma)| , is

Evaluate : |{:( 0, sin alpha , - cos alpha ), ( - sin alpha , 0 , sin beta) , (cos alpha , -sin beta , 0):}|

The points A(0, 0), B(cos alpha, sin alpha) and C(cos beta, sin beta) are the vertices of a right angled triangle if :

Under rotation of axes through theta , x cosalpha + ysinalpha=P changes to Xcos beta + Y sin beta=P then . (a) cos beta = cos (alpha - theta) (b) cos alpha= cos( beta - theta) (c) sin beta = sin (alpha - theta) (d) sin alpha = sin ( beta - theta)

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

The vector cos alpha cos beta hati + cos alpha sin beta hatj + sin alpha hatk is a

Determine the values of alpha, beta, gamma when [{:(0,2sinbeta,tan gamma),(cos alpha, sin beta,-tan gamma),(cos alpha, -sin beta, tan gamma):}] is orthogonal.