A) \[1\]
B) \[2\]
C) \[0\]
D) \[-1\]
Correct Answer: C
Solution :
\[{{\tan }^{2}}\theta +{{\sin }^{2}}\theta +{{\cos }^{2}}\theta -\frac{1}{{{\cos }^{2}}\theta }\] \[=\,{{\tan }^{2}}\theta +{{\sin }^{2}}\theta +{{\cos }^{2}}\theta -{{\sec }^{2}}\theta \] Using \[\left[ \begin{align} & {{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1 \\ & {{\sec }^{2}}\theta -{{\tan }^{2}}\theta =1 \\ \end{align} \right]\] \[=\,\,\,\,\,-{{\sec }^{2}}\theta +{{\tan }^{2}}\theta +{{\sin }^{2}}\theta +{{\cos }^{2}}\theta \] \[=\,\,\,\,\,-({{\sec }^{2}}\theta -{{\tan }^{2}}\theta )+({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )\] \[=\,\,\,\,\,-1+1=\underline{\mathbf{0}}\]
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