Simplify the following expression cosec⁴A(1 - cos⁴ A) - 2cot²A - 1

Solution (By Examveda Team)

$$\eqalign{ & {\text{cose}}{{\text{c}}^4}A\left( {1 - {{\cos }^4}A} \right) - 2{\cot ^2}A - 1 \cr & {\text{Here we take }}A = {45^ \circ } \cr & = {\text{cose}}{{\text{c}}^4}{45^ \circ }\left( {1 - {{\cos }^4}{{45}^ \circ }} \right) - 2{\cot ^2}{45^ \circ } - 1 \cr & = {\left( {\sqrt 2 } \right)^4}\left\{ {1 - {{\left( {\frac{1}{{\sqrt 2 }}} \right)}^4}} \right\} - 2\left( 1 \right) - 1 \cr & = 4\left( {1 - \frac{1}{4}} \right) - 2 - 1 \cr & = 4\left( {\frac{3}{4}} \right) - 2 - 1 \cr & = 3 - 2 - 1 \cr & = 0 \cr} $$