Question

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

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (D)

4

Answer 2

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

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

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