Question 408166

{{{(sec^2(x) + csc^2(x))-(tan^2(x) + cot^2(x))}}}



={{{sec^2(x) + csc^2(x) - tan^2(x) - cot^2(x)}}}......since{{{sec^2x = tan^2(x)+1}}} you will have


={{{tan^2(x) + 1 + csc^2(x) - tan^2(x) - cot^2(x)}}}



={{{cross(tan^2(x)) + 1 + csc^2(x) - cross(tan^2(x)) - cot^2(x)}}}


={{{1 + csc^2x  - cot^2x}}}.........since  {{{csc^2(x)=cot^2(x) + 1}}}....=>...


={{{1 + cot^2(x) + 1  - cot^2(x)}}}


={{{1 + cross(cot^2(x)) + 1  - cross(cot^2(x))}}}


={{{2 }}}