A) 1
B) 19
C) 25
D) 7
Correct Answer: C
Solution :
| [c] \[4{{\sec }^{2}}\theta +9\,\text{cose}{{\text{c}}^{2}}\theta \] \[=4\,(1+ta{{n}^{2}}\theta )+9\,(1+{{\cot }^{2}}\theta )\] \[=13+(4ta{{n}^{2}}\theta +9{{\cot }^{2}}\theta )\] Now, \[AM\ge GM\] \[\Rightarrow \] \[\frac{4{{\tan }^{2}}\theta +9{{\cot }^{2}}\theta }{2}\ge \sqrt{4{{\tan }^{2}}\theta \cdot 9ci{{t}^{2}}\theta }\] \[\Rightarrow \] \[4{{\tan }^{2}}\theta +9{{\cot }^{2}}\theta \ge 2\times \sqrt{36}\ge 12\] \[\therefore \]Minimum value of \[4{{\sec }^{2}}\theta +9\,\text{cose}{{\text{c}}^{2}}\theta =13+12=25\] |
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