Question
Minimum value of $5{\sin ^2}\theta + 4{\cos ^2}\theta $ is
✓
Answer
d
(d) Let $f(\theta ) = 5{\sin ^2}\theta + 4{\cos ^2}\theta = 4 + {\sin ^2}\theta $
(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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