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=`

Explanation

Given,` tanalpha=1/(sqrt(x(x^2+x+1))), tanbeta=(sqrtx)/(sqrt(x^2+x+1)` and `tangamma=sqrt(x^-3+x^-2+x^-1)`

`alpha+beta=gamma`


`tan(alpha+beta)=tan(gamma)`

LHS=`(tan(alpha)+tan(beta)​)/(1−tan(alpha)tan(beta))`

=`(1/(sqrt(x(x^2+x+1)))+(sqrtx)/(sqrt(x^2+x+1)))/(1-1/(sqrt(x(x^2+x+1)))(sqrtx)/(sqrt(x^2+x+1))`

=`(​1/sqrt(x))​×(sqrt(x^2+x+1
)/x)`

...