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

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi, where -1<=x,y,z<=1, then find the value of x^(2)+y^(2)+z^(2)+2xyz

If x tan 30^@ + y cot 60^@ = 0,2x-y tan 45^@ = 1 , then find the value of x and y.

Let tan^(-1)y = tan^(-1)x+tan^(-1)((2x)/(1-x^2)) , where |x| le 1/sqrt3 . Then the value of y is

For x,y,z,t in R , if sin^(-1)x+cos^(-1)y+sec^(-1)z ge t^(2)-sqrt(2pi)*t+3pi , then the value of tan^(-1)x+tan^(-1)y+tan^(-1)z+tan^(-1)( sqrt((2)/(pi))t) is __________.

For x,y,z,t in R , if sin^(-1)x+cos^(-1)y+sec^(-1)z ge t^(2)-sqrt(2pi)*t+3pi , then the value of tan^(-1)x+tan^(-1)y+tan^(-1)z+tan^(-1)( sqrt((2)/(pi))t) is __________.

If ((2x-y)/(x+2y))=(1)/(2), then find the value of ((3x-y)/(3x+y))

If tan^(-1) y = tan^(-1) x + tan^(-1)((2x)/(1 -x^(2)))", where" |x| lt 1/sqrt3 . Then, the value of y is

If sin x=(3)/(5) and tan y=(1)/(2) and if (pi)/(2)

If tan^(2) {pi(x+y)}+cot^(2) {pi (x+y)}=1+sqrt((2x)/(1+x^(2))) where x, y in R , then find the least possible value of y.