If I=`int_(-a)^(a)(alpha sin^(5)x+beta tan^(3)x+gamma cos x)dx`, where `alpha,beta,gamma` are constants, then the value of I depends on

If the integral int_(0)^(10) ([sin2pi x])/(e^(x-[x]))dx=alpha e^(-1)+beta e^(-(1)/(2))+gamma , where alpha, beta, gamma are integers and [x] denotes the greatest integer less than or equal to x, then the value of alpha+beta+gamma is equal to :

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

If tan^(2)alpha tan^(2)beta+tan^(2)beta tan^(2)gamma+tan^(2)gamma tan^(2)alpha+2tan^(2)alpha tan^(2)beta tan^(2)gamma= 1 .(where alpha,beta,gamma in R-{(n pi)/(2)},n in I ) Value of cos2alpha+cos2 beta+cos2gamma is equal to -

If 2 sin alphacos beta sin gamma=sinbeta sin(alpha+gamma),then tan alpha,tan beta and gamma 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 the value of xyz is

Let sin^(-1)alpha+sin^(-1)beta+sin^(-1)gamma=pi and alpha, beta, gamma are non zero real numbers such that (alpha+beta+gamma)(alpha+beta-gamma)=3alphabeta then value of gamma

int_0^10([sin2pix])/e^(-[x]+x)dx=alphae^(-1)+betae^(-1/2)+gamma . then find alpha+beta+gamma

If alpha beta gamma are the roots of x^3+x^2-5x-1=0 then alpha+beta+gamma is equal to