The value of the determinant `{:|(alpha,beta,l), (alpha,x, n),(alpha,beta,x)|:}` is
a. independent of `l`
b. independent of `n`
c.`alpha(x-l)(x-beta)`
d. `alphabeta(x-l)(x-n)`

The value of the determinant |{:(1,sin(alpha-beta)theta,cos (alpha-beta)theta),(a, sinalphatheta,cos alphatheta),(a^(2),sin(alpha-beta)theta,cos(alpha-beta)theta):}| is independent of

The expression (sin(alpha+theta)-"sin"(alpha-theta))/(cos(beta-theta)-cos(beta+theta)) is - independent of alpha b. independent of beta c. independent of theta d. independent of alpha\ a n d\ beta

Find the sum to n terms, whose nth term is tan[alpha+(n-1)beta]tan (alpha+nbeta) .

x+y-ln(x+y)=2x+5 has a vertical tangent at the point (alpha,beta) then alpha+beta is equal to

A real value of x satsifies the equation ((3-4ix)/(3+4ix)) =alpha- ibeta(alpha, beta in R) , if alpha^(2)+beta^(2) is equal to

The value of the determinant |(1,(alpha^(2x)-alpha^(-2x))^2,(alpha^(2x)+alpha^(-2x))^2),(1,(beta^(2x)-beta^(-2x))^2,(beta^(2x)+beta^(-2x))^2),(1,(gamma^(2x)-gamma^(-2x))^2,(gamma^(2x)+gamma^(-2x))^2)| is (a) 0 (b) (alphabeta gamma)^(2x) (c) (alpha beta gamma)^(-2x) (d) None of these

If alpha+beta=pi/2 and beta+ gamma = alpha , then find the value of tan alpha .

If p''(x) has real roots alpha,beta,gamma . Then , [alpha]+[beta]+[gamma] is

If alpha, beta, gamma are the roots of the cubic x^(3)-px^(2)+qx-r=0 Find the equations whose roots are (i) beta gamma +1/(alpha), gamma alpha+1/(beta), alpha beta+1/(gamma) (ii) (beta+gamma-alpha),(gamma+alpha-beta),(alpha+beta-gamma) Also find the valueof (beta+gamma-alpha)(gamma+alpha-beta)(alpha+beta-gamma)

If alpha=e^(i2pi//7)a n df(x)=a_0+sum_(k=1)^(20)a_k x^k , then prove that the value of f(x)+f(alpha, x)++f(alpha^6x) is independent of alphadot