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This question belongs to Arithmetic Ability Trigonometry
Trigonometry
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If $${\text{2}}\sin \theta + {\text{cos}}\theta = \frac{7}{3}{\text{,}}$$    then the value of $$\left( {{\text{ta}}{{\text{n}}^2}\theta - {{\sec }^2}\theta } \right)$$   is?

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Correct Answer: Option B
$$\eqalign{ & {\text{2}}\sin \theta + {\text{cos}}\theta = \frac{7}{3} \cr & \Rightarrow \left( {{\text{ta}}{{\text{n}}^2}\theta - {\text{se}}{{\text{c}}^2}\theta } \right) \cr & \Rightarrow \left( {{{\sec }^2}\theta - 1 - {\text{se}}{{\text{c}}^2}\theta } \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\left[ {\because 1 + {\text{ta}}{{\text{n}}^2}\theta = {{\sec }^2}\theta } \right] \cr & \Rightarrow - 1 \cr} $$
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