Prove that:`|(x+4,x,x),(x,x+4,x),(x,x,x+4)|=16(3x+4)`

Prove that: 4|(x,y),(3x,0)|=3|(x,0),(5x,-4y)|

If |(4+x,4-x,4-x),(4-x,4+x,4-x),(4-x,4-x,4+x)|=0 then find the value of x

Find the value of x if |(1,2x,4x),(1,4,16),(1,1,1)|=0

Find the values of a and b sucht that the function f defined by f(x)= {{:((x-4)/(|x-4|)+a, if x lt 4),(a+b,if x =4),((x-4)/(|x-4|)+b, if x gt 4):} is a continous function at x = 4 .

If sin x + sin^(2) x + sin^(3) x = 1 , then prove that cos^(6)x - 4 cos^(4) x + 8 cos^(2) x - 4 = 0 .

Let f(x) = {((tan x - cot x)/(x-pi/4), ",", x != pi/4),(a, ",", x = pi/4):} The value of a so that f(x) is continuous at x = (pi)/4 , is

If f (x) = (3x + 4)/( 5x -7), g (x) = (7x +4)/(5x -3) then f [g(x)]=