Question 1194262


{{{tan (alpha) + cot (beta) = (1-tan^2(x))/ (1+tan^2(x))}}}.........solve for {{{tan(alpha) }}}

{{{tan (alpha) = (1-tan^2(x))/ (1+tan^2(x)) -cot (beta)}}}............apply trig inverse properties

{{{alpha=tan^-1( (1-tan^2(x))/ (1+tan^2(x)) -cot (beta) )}}}

general solution: 

{{{alpha=tan^-1( (1-tan^2(x))/ (1+tan^2(x)) -cot (beta) ) +2pi}}}