If `alpha+beta=pi/2a n dbeta+gamma=alpha,` then `tanalpha` equals

If alpha < beta < gamma and sin gamma cos alpha=1, where alpha,gamma in[pi,2 pi], then the least integral value of f(x) = | x - alpha| + | x - beta| + |x - gamma| is

If alpha,beta,gamma are the roots of a x^3+b x^2+c x+d=0a n d|alpha beta gamma beta gamma alpha gamma alpha beta|=0,alpha!=beta!=gamma then find the equation whose roots are alpha+beta-gamma,beta+gamma-alpha,a n dgamma+alpha-betadot

If tan beta=2sin alpha sin gamma co sec(alpha+gamma) , then cot alpha,cot beta,cotgamma are in

IF alpha , beta and gamma are angles such that tan alpha + tan beta + tan gamma = tan alpha tan beta tan gamma and x= cos alpha + i sin alpha , y = cos beta + i sin beta and z= cos gamma + i sin gamma , then xyz =

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 )

If tan^2 alpha tan^2 beta + tan^2 beta tan^2 gamma + tan^2 gamma tan^2 alpha + 2 tan^2 alpha tan^2 beta tan^2 gamma = 1 then sin^2 alpha + sin^2 beta + sin^2 gamma =

If tan(alpha-beta)=(sin2beta,)/(3-cos2beta) then (a) tanalpha=2tanbeta (b) tanbeta=2tanalpha (c) 2tanalpha=3tanbeta (d) 3tanalpha=2tanbeta

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

The minimum value of the expression sin alpha + sin beta+ sin gamma , where alpha,beta,gamma are real numbers satisfying alpha+beta+gamma=pi is