Show that the lines `(x-a+d)/(alpha+delta)=(y-a)/alpha =(z-a-d)/(alpha +delta)` and `(x-b+c)/(beta+gamma)=(y-b)/beta=(z-b-c)/(beta+gamma)` are coplanar.

If alpha,beta are the roots of x^2+p x+q=0a n dgamma,delta are the roots of x^2+p x+r=0, then ((alpha-gamma)(alpha-delta))/((beta-gamma)(beta-delta))= a. 1 b. q c. r d. q+r

If "cot"(alpha+beta)=0, then "sin"(alpha+2beta) can be (a) -sinalpha (b) sinbeta (c) cosalpha (d) cosbeta

If alpha,beta,gamma,delta are four complex numbers such that gamma/delta is real and alpha delta - beta gamma !=0 then z = (alpha + beta t)/(gamma+ deltat) represents a A) circle B) parabola C)Ellipse D)straight line

Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),((gamma+alpha-beta-delta)^4,(gamma+alpha-beta-delta)^2,1),((alpha+beta-gamma-delta)^4,(alpha+beta-gamma-delta)^2,1)|=-64(alpha-beta)(alpha-gamma)(alpha-delta)(beta-delta)(gamma-delta)

Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),((gamma+alpha-beta-delta)^4,(gamma+alpha-beta-delta)^2,1),((alpha+beta-gamma-delta)^4,(alpha+beta-gamma-delta)^2,1)|=-64(alpha-beta)(alpha-gamma)(alpha-delta)(beta-delta)(gamma-delta)

If (sin alpha)/(sin beta)=(cos gamma)/(cos delta), then (sin ((alpha-beta)/2) . cos ((alpha+beta)/2) . cos delta)/(sin ((delta-gamma)/2) . sin ((delta+gamma)/2) . sin beta)

alpha,beta,gammaa n ddelta are angle in I, II, III and iv quadrants, respectively and none of them is an integral multiple of pi/2dot They form an increasing arithmetic progression. Which of the following holds? cos(alpha+delta)>0 cos(alpha+delta)=0 cos(alpha+delta) 0orcos(alpha+delta)<0 Which of the following does not hold? sin(beta+gamma)=sin(alpha+delta) sin(beta-gamma)="sin"(alpha-delta) sin(alpha-beta)="tan"(beta-delta) sin(alpha+gamma)=cos2beta) If alpha+beta+gamma+delta=thetaa n dalpha=70^0, then 400^0

If alpha, beta be the roots of x^(2)+x+2=0 and gamma, delta be the roots of x^(2)+3 x+4=0 , then (alpha+gamma)(alpha+delta)(beta+gamma)(beta+delta) is equal to

If ("tan"(theta+alpha))/a=""("tan"(theta+beta))/b=""("tan"(theta+gamma))/c (a+b)/(a-b)sin^2(alpha-beta)+(b+c)/(b-c)sin^2(beta-gamma)+(c+a)/(c-a)sin^2(gamma-alpha)=0

Using properties of determinants in Exercises prove that : {:[( alpha , alpha ^(2) , beta +gamma ),( beta , beta ^(2) , gamma +alpha ),( gamma , gamma ^(2) ,alpha +beta ) ]:} =(beta -gamma ) (gamma -alpha ) (alpha -beta ) (alpha +beta +gamma )