Question

The minimum value of 125tan²θ + 5cot²θ is 

(a) 5

(b) 25

(c) 125

(d) 50

Answer 1

The correct option (d) 50   

Explanation:

given: 125tan²θ + 5cot²θ

if the expression is of type

asin²θ + bcosec²θ 

or

acos²θ + bsec²θ

or

atan²θ + bcot²θ

then minimum value is 2√(ab).

here a = 125 and b = 5.

∴ minimum value is given by 2√(125 × 5) = 50.