" 1) If "tan alpha=(y)/(sqrt(x(x^(2)+x+1)))," tan "beta=(sqrt(x))/(sqrt(x^(2)+x+1))" and "tan gamma=sqrt(x^(-3)+x^(-2)+x^(-1))

If tan alpha = (1)/(sqrt(x(x^(2)+x+1))), tan beta = (sqrt(x))/(sqrt(x^(2)+x+1)) and tan gamma = sqrt(x^(-3)+x^(-2)+x^(-1)) then alpha+beta =

if tan alpha=(1)/(sqrt(x(x^(2)+x+1))),tan beta=(sqrt(x))/(sqrt(x^(2)+x+1)) and tan gamma=sqrt(x^(-3)+x^(-2)+x^(-1)) then alpha+beta=

If tan alpha = 1/sqrt(x(x^(2)+x+1)), tan beta = sqrt(x)/sqrt(x^(2) +x+1) and tan gamma = sqrt(x^(-3) + x^(-2) + x^(-1)) , then alpha + beta=

If tan alpha=(1)/(sqrt(x(x^(2)+x+1))),tan beta=(sqrt(x))/(sqrt(x^(2)+x+1)) and tan gamma=sqrt((1)/(x^(3))+(1)/(x^(2))+(1)/(x)) be such that l alpha+m beta+n gamma=0 then the value of l^(3)+m^(3)+n^(3)-3lmn is

If tan alpha = (1)/(sqrt (x (x ^(2) + x + 1))). tan beta = (sqrtx)/(sqrt (x ^(2) + x +1))and tan y = (x ^(-3) + x ^(-2)+ x ^(-1)) ^(1//2), then for x gt 0

If tan A= 1/(sqrt(x(x^2+x+1))), tan B = sqrtx/(sqrt (x^2+ x+ 1)) and tan C = sqrt(x^(-3)+x^(-2)+x^(-1)) , prove that A+B=C.

"tan^(-1)"((sqrt(x)-x)/(1+sqrt(x^(3))))"

If tan A = frac{1}{sqrt (x(x^2 x 1)} , tan B = frac{sqrt x}{sqrt (x^2 x 1)} , and tan C = (x^(-3) x^(-2) x^(-1))^(1/2) , 0 < A, B, C < pi/2 , then A B is equal to :

int(1+tan^(2)x)/(sqrt(tan^(2)x+3))

tan^(-1)(x+sqrt(1+x^(2)))=