For `0ltx ,yltpi,`the number of ordered pairs `(x, y)` satisfying system equations `cot^2(x-y)-(1+sqrt(3))cot(x-y)+sqrt(3)="0 and cosy="(sqrt(3))/2`is

The number of ordered pairs (x,y) satisfying |x|+|y|=2 and sin""((pix^(2))/(3))=1 is/are

If x, y in [0,2pi] then find the total number of order pair (x,y) satisfying the equation sinx .cos y = 1

The number of all possible ordered pairs (x, y), x, y in R satisfying the system of equations x+y=(2pi)/3, cosx+cosy=3/2 is

The number of ordered pairs which satisfy the equation x^2+2xsin(x y)+1=0 are (where y in [0,2pi] ) (a) 1 (b) 2 (c) 3 (d) 0

The locus of the point P(x,y) satisfying the relation sqrt((x-3) ^(2) +(y-1)^(2))+ sqrt((x+3) ^(2) +(y-1)^(2))=6 is-

If x , y , z are natural numbers such that cot^(-1)x+cot^(-1)y=cot^(-1)z then the number of ordered triplets (x , y , z) that satisfy the equation is 0 (b) 1 (c) 2 (d) Infinite solutions

3 cot ^(-1)""(1)/(2-sqrt(3))+cot ^(-1)""x=(pi)/(2)

A beam of light is sent along the line x-y=1 , which after refracting from the x-axis enters the opposite side by turning through 30^0 towards the normal at the point of incidence on the x-axis. Then the equation of the refracted ray is (a) (2-sqrt(3))x-y=2+sqrt(3) (b) (2+sqrt(3))x-y=2+sqrt(3) (c) (2-sqrt(3))x+y=(2+sqrt(3)) (d) y=(2-sqrt(3))(x-1)