Question

The minimum value of $64\sec \theta +27\cos ec\theta$ when $\theta$ lies in $(0,\frac{\pi }{2})$ is

• A. $125$
• B. $625$
• C. $25$
• D. $1025$

Answer 1

The correct option is A $125$

$5^3(\frac{(4{)}^3}{5^3}sec\theta +\frac{3^3}{5^3}cosec\theta )$
Let $tan\varphi =\frac{3}{4}$
$5^3(co{s}^3\varphi sec\theta +si{n}^3\varphi cosec\theta )$
Minimum If $\varphi =\theta$
$5^3(co{x}^2\varphi +si{n}^2\varphi )$
$=125$