Minimum value of 8cos^2x + 18sec^2x , , x R wherever it is define… - Vidyadip

MCQ

Minimum value of $8cos^2x + 18sec^2x \,\,\forall x \in R$ wherever it is defined, is :

A
$24$
B
$25$
✓
$26$
D
$18$

✓

Answer

Correct option: C.

$26$

c
$y = 8\, cos^2x + 18\, sec^2x$

$= 8 (cos^2x + sec^2x) + 10\, sec^2x$

$= 8 [ (cos x - sec x )^2 + 2 ] + 10\, sec^2x$

where $cosx = secx$ $\Rightarrow$ $ x = 0$

$y_{min} = 16 + 10 = 26$

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