Prove that `|[x+4,2x,2x],[2x,x+4,2x],[2x,2x,x+4]|=(5x+4)(4-x)^2`

By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x-4)(4-x)^2 (ii) |(y+k,y,y),(y,y+k,y),(y,y,y+k)|=k^2(3y+k)

By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x-4)(4-x)^2 (ii) |(y+k,y,y),(y,y+k,y),(y,y,y+k)|=k^2(3y+k)

By using properties of determinants, prove the following |(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x+4)(4-x)^2

By using properties of determinants, prove the following: |x+4 2x2x2xx+4 2x2x2xx+4|=(5x+4)(4-x)^2

If |(x-4,2x,2x),(2x,x-4,2x),(2x,2x,x-4)|=(A+Bx)(x-A)^2 then the ordered pair (A,B) is equal to

Prove the identities: |[z, x, y],[ z^2,x^2,y^2],[z^4,x^4,y^4]|=|[x, y, z],[ x^2,y^2,z^2],[x^4,y^4,z^4]|=|[x^2,y^2,z^2],[x^4,y^4,z^4],[x, y, z]| =x y z (x-y)(y-z)(z-x)(x+y+z)

Prove: |(z, x, y),( z^2,x^2,y^2),(z^4,x^4,y^4)|=|(x, y, z),( x^2,y^2,z^2),(x^4,y^4,z^4)|=|(x^2,y^2,z^2),(x^4,y^4,z^4),(x, y, z)|=x y z(x-y)(y-z)(z-x)(x+y+z) .

Prove that : |{:(x+a,x+2a,x+3a),(x+2a,x+3a,x+4a),(x+4a,x+5a,x+6a):}|=0

Prove that: sin2x+2sin4x+sin6x=4cos^2xsin4

prove that sin2x+2sin4x+sin6x=4cos^(2)x.sinx