Class 11

Math

Algebra

Sequences and Series

The least value of $21 +32 cosec_{2}θ+83 sec_{2}θ$ is

- $2413 $
- $4861 $
- $2561 $
- $2461 $

$=21 +32 +32 cot_{2}θ+83 +83 tan_{2}θ$

$=2437 +32 cot_{2}θ+83 tan_{2}θ$

Now, AM$≥$GM

$232 cot_{2}θ+83 tan_{2}θ ≥32 cot_{2}θ×83 tan_{2}θ $

$32 cot_{2}θ+83 tan_{2}θ≥1$

Therefore, $2437 +32 cot_{2}θ+83 tan_{2}θ≥2437 +1=2461 $

Hence, option 'D' is correct.