For the equation `1-2x-x^2=tan^2(x+y)+cot^2(x+y)` (a)exactly one value of `x` exists (b)exactly two values of `x` exists (c)`y=-1+npi+pi/4,n in Z` (d)`y=1+npi+pi/4, n in Z`

Equation 1+x^2+2x"sin"(cos^(-1)y)=0 is satisfied by (a) exactly one value of x (b) exactly two value of x (c) exactly one value of y (d) exactly two value of y

If x+y=pi//4 and tan x+tan y=1 , then (n in Z)

If tan^(2)(x+y)+cot^(2)(x+y)=1-2x-x^(2), then (where, n in Z )

If the system of equations x+y+z=1,x+2y+4z=n and x+4y+10z=n^(2) .are consistent, then the sum of the values of n is-...

If the line (x-4)/(1)=(y-2)/(1)=(z-k)/(2) lies exactly on the plane 2x-4y+z=7 , the value of k is

The line (x-4)/1=(y-2)/1=(z-k)/2 lies exactly on the plane 2x-4y+z=7 then the value of k is (A) 7 (B) -7 (C) 1 (D) none of these

If the lines (x-2)/(1)=(y-3)/(1)=(x-4)/(-k) and (x-1)/(k)=(y-4)/(2)=(x-5)/(1) are coplanar,then k can have (1) exactly one value (2) exactly two values (3) exactly three values (4) any value

There are two circles whose equation are x^(2)+y^(2)=9 and x^(2)+y^(2)-8x-6y+n^(2)=0,n in Z. If the two circles have exactly two common tangents,then the number of possible values of n is 2 (b) 8 (c) 9 (d) none of these

If alpha,beta, gamma re the roots of the equations x^3+px^2+2x+p=0 then the general value of tan^-1 alpha+tan^-1 beta+tan^-1 gamma is (A) npi (B) (npi)/2 (C) (2n+1) pi/2 (D) dependent upon the value of p.

If tan^(-1)((1)/(y))=-pi+cot^(-1)y, where y=x^(2)-3x+2, then find the value of x