Simplify the following expression cosec4A(1 - cos4 A) - 2cot2A - 1
A. sin2A
B. cosec2A
C. 1
D. 0
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & {\text{cose}}{{\text{c}}^4}A\left( {1 - {{\cos }^4}A} \right) - 2{\cot ^2}A - 1 \cr & {\text{Here we take }}A = {45^ \circ } \cr & = {\text{cose}}{{\text{c}}^4}{45^ \circ }\left( {1 - {{\cos }^4}{{45}^ \circ }} \right) - 2{\cot ^2}{45^ \circ } - 1 \cr & = {\left( {\sqrt 2 } \right)^4}\left\{ {1 - {{\left( {\frac{1}{{\sqrt 2 }}} \right)}^4}} \right\} - 2\left( 1 \right) - 1 \cr & = 4\left( {1 - \frac{1}{4}} \right) - 2 - 1 \cr & = 4\left( {\frac{3}{4}} \right) - 2 - 1 \cr & = 3 - 2 - 1 \cr & = 0 \cr} $$Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
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