Without expanding, show that the value of each of the determinants is zero: `|"cos"(x+y)-sin(x+y)cos2ysinxcosxsiny-cosxsinx-cosy|`

Without expanding, show that the value of each of the determinants is zero: |"cos"(x+y) \-sin(x+y) \cos2y\ sinx\ cosx\ siny\ -cosx \ sinx \ -cosy|

|[cos(x+y),-sin(x+y),cos2y],[sin x,cos x,sin y],[-cos x,sin x,-cos y]|=

Without expanding, show that the value of each of the determinants is zero: |sinalphacosalpha"cos"(alpha+delta)sinbetacosbeta"cos"(beta+delta)singammacosgamma"cos"(gamma+delta)|

Without expanding,show that the value of each of the determinants is zero: det[[sin alpha,cos alpha,cos(alpha+delta)sin beta,cos beta,cos(beta+delta)sin gamma,cos gamma,cos(gamma+delta)]]

Without expanding,show that the values of the following determinants are zero: |(x,y,z),(x+3a,y+3b,z+3c),(a,b,c)|

Without expanding,show that the values of the following determinants are zero: |(1,4,y+z),(1,4,z+x),(1,4,x+y)|

Without expanding,show that the values of the following determinants are zero: |(1,x,x^2-yz),(1,y,y^2-zx),(1,z,z^2-xy)|

Find the value of the determinant |"cos"(x-y)"cos"(y-z)"cos"(z-x)"cos"(x+y)"cos"(y+z)cos(z+x)"sin"(x+y)"sin"(y+z)s in(z+x)|

Show that value of the determinant a,sin x,cos x-sin x,-a,1cos x,1,a]| is independent of x.