Question 1190066


Given:

{{{tan(x)=a/b}}}

{{{sin(x)/cos(x) = a/b }}}=>{{{sin(x)=a}}} and {{{cos(x) =b}}}


we will have real solution if

{{{b<>0}}}, {{{a>0}}}, {{{b>=0}}} when {{{180}}}° ≤ {{{x}}} ≤ {{{270}}}°


use identity:

{{{ cos(4x)=sin^4(x) + cos^4(x) - 6 sin^2(x) cos^2(x)}}}


{{{ cos(4x)=a^4 + b^4 - 6a^2* b^2}}}


{{{cos(4x)=(a^2 - 2ab - b^2) (a^2 + 2ab - b^2)}}}