Question : The minimum value of $2\sin^{2}\theta+3\cos^{2}\theta$ is:
Option 1: 0
Option 2: 3
Option 3: 2
Option 4: 1
Answer (1)
20th Jan, 2024
Correct Answer: 2
Solution :
Given: $2\sin^{2}\theta+3\cos^{2}\theta$
= $2\sin^{2}\theta+3(1-\sin^{2}\theta)$
= $2\sin^{2}\theta+3-3\sin^{2}\theta)$
= $3-\sin^{2}\theta$
For minimum value of $(3-\sin^{2}\theta)$ by putting $\sin^{2}\theta=1$
⇒ $3-1=2$
Hence, the correct answer is 2.
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