" 4"quad 2^(x)=3^(y)=12^(2)*sin(1)" that "(1)/(2)=(1)/(y)+(2)/(x)

If (2+sin x)(dy)/(dx)+(y+1)cos x=0 and y(0)=1, then y((pi)/(2)) is equal to -(1)/(3)(2)(4)/(3) (3) (1)/(3)(4)-(2)/(3)

If y=sin^(-1)x, show that (d^(2)y)/(dx^(2))=(1)/((1-x^(2))^(3/2))

If A=[[0,1,3],[1,2,x],[2,3,1]] and A^(-1)=[[(1)/(2),-4,(5)/(2)],[-(1)/(2),3,-(3)/(2)],[(1)/(2),y,(1)/(2)]] . Find x,y

The mirror image of the parabola y^(2)=4x in the tangent to the parabola at the point (1,2) is (a)(x-1)^(2)=4(y+1)(b)(x+1)^(2)=4(y+1)(c)(x+1)^(2)=4(y-1) (d) (x-1)^(2)=4(y-1)

If Sin^(-1)x + Sin^(-1)y + Sin^(-1)z = pi , then prove that x^(4) + y^(4) + z^(4) + 4x^(2)y^(2)z^(2) = 2(x^(2)y^(2)+y^(2)z^(2)+z^(2)x^(2)) .

If y=(1+cos2x)/(3-2sin2x)," then "(3-2sin2x)^(2)y_(1)=