2^((1)/(cos^(2)x))sqrt(y^(2)-y+(1)/(2))<=1

Solve for x and y : 2^(1/cos^2x)sqrt(y^2-y+1//2) le 1

The equation |sqrt(x^(2)+(y-1)^(2))-sqrt(x^(2) +(y+1)^(2))| = k will represent a hyperbola for-

Identify the curve sqrt((x+1)^(2)+y^(2))+ sqrt(x^(2)+(y-1)^(2))-2 =0

Identify the curve sqrt((x+1)^(2)+y^(2))+ sqrt(x^(2)+(y-1)^(2))-2 =0

Equation of a line which is tangent to both the curve y=x^(2)+1 and y=x^(2) is y=sqrt(2)x+(1)/(2) (b) y=sqrt(2)x-(1)/(2)y=-sqrt(2)x+(1)/(2)(d)y=-sqrt(2)x-(1)/(2)

If tan^(-1)x+cos^(-1)((y)/(sqrt(1+y^(2))))=sin^(-1)((3)/(sqrt(10))) , then

sin^(-1)x+sin^(-1)y=cos^(-1)(sqrt(1-x^(2))sqrt(1-y^(2))-xy) if x in[0,1],y in[0,1]

Cos^(-1)(xy-sqrt(1-x^(2))sqrt(1-y^(2)))=

sin^(-1)x+sin^(-1)y=cos^(-1)""{sqrt((1-x^(2))(1-y^(2)))-xy}

If y = cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2) , -1/2ltxlt0 , find (dy)/(dx)