Minimum value of 5 ^2 + 4 ^2 is - Vidyadip

MCQ

Minimum value of $5{\sin ^2}\theta + 4{\cos ^2}\theta $ is

A
$1$
B
$2$
C
$3$
✓
$4$

✓

Answer

Correct option: D.

$4$

d
(d) Let $f(\theta ) = 5{\sin ^2}\theta + 4{\cos ^2}\theta = 4 + {\sin ^2}\theta $

$\therefore f(\theta ) \ge 4 + 0$ $( \because {\sin ^2}\theta \ge 0)$

$\therefore $ The minimum value of $f(\theta )$ is $4.$

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