Question

The minimum value of $2 \sin^2 \theta + 3 \cos^2 \theta$ is

• A. 3
• B. 0
• C. 1
• D. 2

Answer 1

Answer: (D)

2

Answer 2

The expression $2 \sin^2 \theta + 3 \cos^2 \theta$ can be rewritten as $2 \sin^2 \theta + 3 (1 - \sin^2 \theta) = 2 \sin^2 \theta + 3 - 3 \sin^2 \theta = 3 - \sin^2 \theta$.

Since $0 \le \sin^2 \theta \le 1$, to find the minimum value of $3 - \sin^2 \theta$, we must subtract the maximum possible value of $\sin^2 \theta$, which is 1.

So, the minimum value is $3 - 1 = 2$.