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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?
Answer & Solution
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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