Question

The least value of $2{\sin }^2\theta +3{\cos }^2\theta$ is

• A. $1$
• B. $2$
• C. $3$
• D. $5$

Answer 1

The correct option is B

$2$

Solve the given expression

Given expression, $2{\sin }^2\theta +3{\cos }^2\theta$

$=2(1-{\cos }^2\theta )+3{\cos }^2\theta$ $[\because {\sin }^2\theta +{\cos }^2\theta =1]$

$$\begin{gathered} =2-2{\cos }^2\theta +3{\cos }^2\theta \\ =2+{\cos }^2\theta \end{gathered}$$

Now, the minimum value will be obtained, when the value of ${\cos }^2\theta =0$

Therefore, the least value of$2{\sin }^2\theta +3{\cos }^2\theta =2$ , so, option (B) is the correct answer.