If $b _{ n }=\int \limits_{0}^{\frac{\pi}{2}} \frac{\cos ^{2} nx }{\sin x } dx , n \in N$, then
If $b _{ n }=\int \limits_{0}^{\frac{\pi}{2}} \frac{\cos ^{2} nx }{\sin x } dx , n \in N$, then
- [JEE MAIN 2022]
- A
$b_{3}-b_{2}, b_{4}-b_{3}, b_{5}-b_{4}$ are in an $A.P.$ with common difference $-2$
- B
$\frac{1}{ b _{3}- b _{2}}, \frac{1}{ b _{4}- b _{3}}, \frac{1}{ b _{5}- b _{4}}$ are in an $A.P.$ with common difference $2$
- C
$b _{3}- b _{2}, b _{4}- b _{3}, b _{5}- b _{4}$ are in a $G.P.$
- D
$\frac{1}{b_{3}-b_{2}}, \frac{1}{b_{4}-b_{3}}, \frac{1}{b_{5}-b_{4}}$ are in an $A.P.$ with common difference $-2$
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- [JEE MAIN 2021]