Question

The least value of 8 cosec²θ + 25 sin² θ is:

• A. $$10\sqrt{2}$$
• B. $$40\sqrt{2}$$
• C. $$20\sqrt{2}$$
• D. $$30\sqrt{2}$$

Answer 1

Answer:

$$20\sqrt{2}$$

Solution:

Given:

8 cosec²θ + 25 sin² θ

Formula:

The minimum value of "a cosec²θ + b sin² θ" is given by $2\sqrt{ab}$

Calculation:

Minimum Value of 8 cosec²θ + 25 sin² θ $=2\sqrt{(8\times{25}})$

$=2\sqrt{200}$

$=2\sqrt{(100\times{2}})$

$=2\times{10}\sqrt{2}$

$=20\sqrt{2}$