By using properties of determinants , show that : ` {:[( 1,x,x^(2) ),( x^(2) ,1,x) ,( x,x^(2), 1) ]:} =( 1-x^(3)) ^(2) `

If y=e^(tan^(-1)x) , show that (1+x^(2))y''+(2x-1)y'=0 .

If y=e^(tan^(-1)x) , show that (1+x^(2))y''+(2x-1)y'=0

Show that : tan (cos^(-1)x) = (sqrt(1-x^(2)))/x

If y= (tan^(-1)x)^(2) , show that (x^(2)+1)^(2) y_(2)+2x(x^(2)+1)y_(1)=2 .

Without expanding a determinant at any stage, show that | |x^2+x ,x+1 , x+2|,|, 2x^2+3x-1, 3x , 3x-3 | , | x^2+2x+3, 2x-1 ,2x-1||=x A+B ,w h e r eAa n dB are determinant of order 3 not involving xdot

(3x - 9)/( (x - 1 )(x + 2 )(x^(2)+1))

Show that |(1,1,1),(x,y,z),(x^(2),y^(2),z^(2))|=(x-y)(y-z)(z-x)

Divide (2x^(2) + x-3)/((x-1)^(2)) " by " (2x^(2) + 5x +3)/(x^(2)-1)

If x in (0, 1) , then find the value of tan^(-1) ((1 -x^(2))/(2x)) + cos^(-1) ((1 -x^(2))/(1 + x^(2)))