A) \[0\]
B) \[1\]
C) \[-1\]
D) \[\frac{1}{2}\]
Correct Answer: B
Solution :
\[{{\tan }^{2}}\theta \,\,se{{c}^{2}}\theta ({{\cot }^{2}}\theta -{{\cos }^{2}}\theta )\] \[={{\sec }^{2}}\theta ({{\tan }^{2}}\theta {{\cot }^{2}}\theta -{{\tan }^{2}}\theta {{\cos }^{2}}\theta )\] \[={{\sec }^{2}}\theta \left( 1-\frac{{{\sin }^{2}}\theta }{{{\cos }^{2}}\theta }{{\cos }^{2}}\theta \right)={{\sec }^{2}}\theta (1-{{\sin }^{2}}\theta )\] \[={{\sec }^{2}}\theta .\,{{\cos }^{2}}\theta =1\]
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