If `A(cos alpha,sin alpha), B(cos beta, sin beta), C(cosgamma,sin gamma)` are vertices of `Delta`ABC having ortho centre at origin then find the value of `sumcos(alpha-beta).`

P(cosalpha,sinalpha), Q(cosbeta, sinbeta) , R(cosgamma, singamma) are vertices of triangle whose orthocenter is (0, 0) then the value of cos(alpha-beta) + cos(beta-gamma) + cos(gamma-alpha) is

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 :

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

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

If alpha and beta are roots of the equation a cos theta + b sin theta = c , then find the value of tan (alpha + beta).

If sin alpha cos beta=-(1)/(2) then find the range of values of cos alpha sin beta

If A=[(cos^(2)alpha, cos alpha sin alpha),(cos alpha sin alpha, sin^(2)alpha)] and B=[(cos^(2)betas,cos beta sin beta),(cos beta sin beta, sin^(2) beta)] are two matrices such that the product AB is null matrix, then alpha-beta is

If a = cos 2 alpha + i sin 2 alpha , b= cos 2 beta + i sin 2 beta , c = cos 2 gamma + i sin 2 gamma and d = cos2 delta + i sin 2 delta then sqrt( abcd) + 1/sqrt( abcd) is :

If 2 sin alphacos beta sin gamma=sinbeta sin(alpha+gamma),then tan alpha,tan beta and gamma are in

If a=cos alpha+i sin alpha, b=cos beta+isin beta,c=cos gamma+i sin gamma and b/c+c/a+a/b=1, then cos(beta-gamma)+cos(gamma-alpha)+cos(alpha-beta)=