Let `f(x)=|(4x+1,-cosx,-sinx),(6,8sinalpha,0),(12sinalpha, 16sin^(2)alpha,1+4sinalpha)|` and `f(0)=0`. If the sum of all possible values of `alpha` is `kpi` for `alpha in [0, 2pi]`, then the value of k is equal to

A=[(sinalpha,0),(0,sinalpha)] and det(A^2-1/2I)=0 , then a possible value of alpha is

Let A(alpha)=[(cos alpha, 0,sin alpha),(0,1,0),(sin alpha, 0, cos alpha)] and [(x,y,z)]=[(0,1,0)] . If the system of equations has infinite solutions and sum of all the possible value of alpha in [0, 2pi] is kpi , then the value of k is equal to

Let A(alpha)=[(cos alpha, 0,sin alpha),(0,1,0),(sin alpha, 0, cos alpha)] and [(x,y,z)]=[(0,1,0)] . If the system of equations has infinite solutions and sum of all the possible value of alpha in [0, 2pi] is kpi , then the value of k is equal to

If A = ({:(0, sin alpha),(sinalpha,0):}) and det ( A^(2) - ( 1)/( 2) I )=0 , then a possible value of alpha is :

Let A_(alpha)=[(cosalpha, -sinalpha,0),(sinalpha, cosalpha, 0),(0,0,1)] , then :

Let A_(alpha)=[(cosalpha, -sinalpha,0),(sinalpha, cosalpha, 0),(0,0,1)] , then :

If sinalpha, sin^2alpha, 1 , sin^4alpha and sin^6alpha are in A.P., where -pi < alpha < pi, then alpha lies in the interval

If alpha in [pi/2,pi] , then the value of sqrt(1+sin alpha)- sqrt(1-sinalpha) is equal to:

If sin.alpha/2+cos.alpha/2=1.4, then: sinalpha=

Let A=({:(cosalpha,-,sinalpha),(sinalpha,,cosalpha):}),(alphaepsilonR) such that A^(32)=({:(0,-1),(1,0):}) . Then a value of alpha is: