`2x -y gt 1 , x - 2y lt -1`

2x - y gt 1, 2y - x gt 1

Which of the folowing should be the feasible region of the system of linear lnequalities x + 2y lt= 12 , 2x + y lt= 12 , 4x +5y gt= 20 and x,y gt= 0 ?

Prove that tan{1/2sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)((1-y^(2))/(1+y^(2)))}=(x+y)/(1-xy) , where |x| lt 1,y gt 0 and xy lt 1 .

Find the values of the following tan frac(1)(2) [sin^(-1)((2x)/(1+x^2))+ cos^(-1) ((1-y^2)/(1+y^2))],|x| lt 1, y gt 0 and x y lt 1

Solve the following systems of linear inequalities graphically : x lt y, x gt 0 , y lt 1 .

Find the value of "tan" (1)/(2)[ "sin"^(-1)(2x)/(1+x^(2)) +"cos"^(-1) (1-y^(2))/(1+y^(2))], |x| lt 1, y gt 0 and xy lt 1 .

Solve the following systems of linear inequalities graphically : x gt y , x lt 1, y gt 0 .

If x^(2) - y^(2) = 1, (x gt y) then find the value of log_(x-y) (x+y)