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x=(1)/(2)y-2quad y=1-x...

x=(1)/(2)y-2quad y=1-x

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If x_(1),x_(2) "and" y_(1),y_(2) are the roots of the equations 3x^(2) -18x+9=0 "and" y^(2)-4y+2=0 the value of the determinant |{:(x_(1)x_(2),y_(1)y_(2),1),(x_(1)+x_(2),y_(1)+y_(2),2),(sin(pix_(1)x_(2)),cos (pi//2y_(1)y_(2)),1):}| is

If x_(1),x_(2) "and" y_(1),y_(2) are the roots of the equations 3x^(2) -18x+9=0 "and" y^(2)-4y+2=0 the value of the determinant |{:(x_(1)x_(2),y_(1)y_(2),1),(x_(1)+x_(2),y_(1)+y_(2),2),(sin(pix_(1)x_(2)),cos (pi//2y_(1)y_(2)),1):}| is

If x_(1),x_(2) "and" y_(1),y_(2) are the roots of the equations 3x^(2) -18x+9=0 "and" y^(2)-4y+2=0 the value of the determinant |{:(x_(1)x_(2),y_(1)y_(2),1),(x_(1)+x_(2),y_(1)+y_(2),2),(sin(pix_(1)x_(2)),cos (pi//2y_(1)y_(2)),1):}| is

If x_(1),x_(2) "and" y_(1),y_(2) are the roots of the equations 3x^(2) -18x+9=0 "and" y^(2)-4y+2=0 the value of the determinant |{:(x_(1)x_(2),y_(1)y_(2),1),(x_(1)+x_(2),y_(1)+y_(2),2),(sin(pix_(1)x_(2)),cos (pi//2y_(1)y_(2)),1):}| is

Let x+(1)/(x)=2, y+(1)/(y)=-2 and sin^(-1)x+cos^(-1)y=m pi , then the value of m is

Let x+(1)/(x)=2, y+(1)/(y)=-2 and sin^(-1)x+cos^(-1)y=m pi , then the value of m is

The solution of (dy)/(dx)=((x-1)^(2)+(y-2)^(2)tan^(-1)((y-2)/(x-1)))/((xy-2x-y+2)tan^(-1)((y-2)/(x-1))) is equal to

Prove that the line passing through the points (x_(1),y_(1)) and (x_(2),y_(2)) is at a distance of |(x_(1)y_(2)-x_(2)y_(1))/(sqrt((x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)))| from origin.

Prove that the line passing through the points (x_(1),y_(1)) and (x_(2),y_(2)) is at a distance of |(x_(1)y_(2)-x_(2)y_(1))/(sqrt((x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)))| from origin.

If x=sintheta , y=cosptheta , prove that (1-x^2)y_2-x y_1+p^2y=0 , where y_2=(d^2y)/(dx^2) and y_1=(dy)/(dx) .