(" iv ")x+y=xy^(3)

If cottheta+tantheta=x and sectheta-costheta=y then (i) sintheta costheta=-x (ii) sintheta tantheta=-y (iii) (x^2y)^(2/3)-(xy^2)^(2/3)=1 (iv) (x^2y)^(1/3)+(xy^2)^(1/3)=1

Find the following products: (6x)/(5)(x^(3)+y^(3)) (ii) xy(x^(3)-y^(3))0.1y(0.1x^(5)+0.1y)( iv) (8)/(27)xyz((3)/(2)xyz^(2)-(9)/(4)xy^(2)z^(3))

Factorise : (iv) xy^(2) + (x-1)y-1

Given x = 2 - 3i and y = 4 + i . Find (i) xy " "(ii) x + y " " (iii) x - y " "(iv) x/y " " (v) (barx)/y " "(vi) (x-y)^(2)

Verify : (i) x^(3)+y^(3)=(x+y)(x^(2)-xy+y^(2)) " " (ii) x^(3)-y^(3)=(x-y)(x^(2)+xy+y^(2))

Veriffy : (i) x^(3)+y^(3)=(x+y)(x^(2)-xy+y^(2))x^(3)-y^(3)=(x-y)(x^(2)+xy+y^(2))

Verify : (i) x^(3)+y^(3)=(x+y)(x^(2)-xy+y^(2)) (ii) x^(3)-y^(3)=(x-y)(x^(2)+xy+y^(2))

The solution of the differential equation y'(y^(2)-x)=y is a) y^(3)-3xy=C b) y^(3)+3xy=C c) x^(3)-3xy=C d) y^(3)-xy=C

x^(3) + xy^(2) - x^(2) y - y^(3) = "_______"