Solve for x : `|(1,1,1),(1,x,1),(1,1,x)|=0`

Solve for x : |(2+x,3,1),(3,1+x,2),(1,2,3+x)|=0

Solve for x : |(x^2,x,1),(4,2,1),(9,3,1)|+|(x^2,x,-1),(4,2,-1),(9,3,-1)|=0

Solve for x : [(x,1)][(1,0),(-2,-3)][(x),(5)]=[0]

Solve for x : tan^-1(1+x)+tan^-1(1-x)=pi/4

Solve for x, tan^(-1)(x+1) +tan^(-1) (x-1) =tan^(-1) ((8)/(31)) .

Solve for x : tan^-1(x-1)+tan^-1 x+tan^-1(x+1)=tan^-1 3x

Solve for x, tan^(-1)((2x)/(1-x^(2)))+cot^(-1)((1-x^(2))/(2x))=(pi)/(3), -1 lt x lt 1 .

Examine the continuity of the following function at the given point : f(x) = {(x, 0 le x < 1/2),(1, x = 1/2),(1-x, 1/2 < x < 1):} at x = 1/2 .

Evaluate : |(x^2-x+1,x-1),(x+1,x+1)| .