The value of $$\left[ {\frac{{{\text{co}}{{\text{s}}^2}{\text{A}}\left( {{\text{sin A}} + {\text{cos A}}} \right)}}{{{\text{cose}}{{\text{c}}^2}{\text{A}}\left( {{\text{sin A}} - {\text{cos A}}} \right)}} + \frac{{{\text{si}}{{\text{n}}^2}{\text{A}}\left( {{\text{sin A}} - {\text{cos A}}} \right)}}{{{\text{se}}{{\text{c}}^2}{\text{A}}\left( {{\text{sin A}} + {\text{cos A}}} \right)}}} \right]$$         $$\left( {{\text{se}}{{\text{c}}^2}{\text{ A}} - {\text{cose}}{{\text{c}}^2}{\text{ A}}} \right) = ?$$

Solution(By Examveda Team)

  $$\left[ {\frac{{{\text{co}}{{\text{s}}^2}{\text{A}}{\text{.si}}{{\text{n}}^2}{\text{A}}\left( {{\text{sin A}} + {\text{cos A}}} \right)}}{{\left( {{\text{sin A}} - {\text{cos A}}} \right)}} + \frac{{{\text{si}}{{\text{n}}^2}{\text{A}}{\text{.co}}{{\text{s}}^2}{\text{A}}\left( {{\text{sin A}} - {\text{cos A}}} \right)}}{{\left( {{\text{sin A}} + {\text{cos A}}} \right)}}} \right]$$           $$\left[ {\frac{1}{{{\text{co}}{{\text{s}}^2}{\text{A}}}} - \frac{1}{{{\text{si}}{{\text{n}}^2}{\text{A}}}}} \right]$$
  $$ \Rightarrow \left[ {\frac{{{{\left( {{\text{sin A}} + {\text{cos A}}} \right)}^2} + {{\left( {{\text{sin A}} - {\text{cos A}}} \right)}^2}}}{{\left( {{\text{sin A}} - {\text{cos A}}} \right)\left( {{\text{sin A}} + {\text{cos A}}} \right)}}} \right]$$       $$\left( {{\text{si}}{{\text{n}}^2}{\text{ A}} - {\text{co}}{{\text{s}}^2}{\text{ A}}} \right)$$
$$\eqalign{ & \Rightarrow 2\left( {{\text{si}}{{\text{n}}^2}{\text{ A}} + {\text{co}}{{\text{s}}^2}{\text{ A}}} \right) \cr & \Rightarrow 2 \cr} $$