The value of sec⁴A(1 - sin⁴A) - 2tan²A is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{According to the question ,}} \cr & {\text{ se}}{{\text{c}}^4}{\text{A}}\left( {1 - {{\sin }^4}{\text{A}}} \right) - 2{\text{ta}}{{\text{n}}^2}{\text{A}} \cr & {\text{Put A}} = {45^ \circ } \cr & \Rightarrow {\text{ se}}{{\text{c}}^4}{45^ \circ }\left( {1 - {{\sin }^4}{{45}^ \circ }} \right) - 2{\text{ta}}{{\text{n}}^2}{45^ \circ } \cr & \Rightarrow 4\left( {1 - \frac{1}{4}} \right) - 2 \cr & \Rightarrow 4 \times \frac{3}{4} - {\text{2}} \cr & \Rightarrow 3 - 2 \cr & \Rightarrow 1 \cr} $$