[" EXAMPLE "16" If "tan alpha=(1)/(sqrt(x(x^(2)+x+1)))" tan "beta=(sqrt(x))/(sqrt(x^(2)+x+1))" and "tan y=sqrt(x^(-3)+x^(-2)+x)],[" prove that "alpha+beta=gamma" ."]

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 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.

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 tanalpha=1/(sqrt(x(x^2+x+1))), tanbeta=(sqrtx)/(sqrt(x^2+x+1) and tangamma=sqrt(x^-3+x^-2+x^-1) then alpha+beta=

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 alpha=tan^(-1)((sqrt(3)x)/(2y-x)),beta=tan^(-1)((2x-y)/(sqrt(3y)))" then "alpha-beta=

If tan^(-1). (sqrt((1+x^(2))) - sqrt((1-x^(2))))/(sqrt((1+x^(2)))+sqrt((1-x^(2))))=alpha" , then " x^(2) is