Question

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

• A. $1$
• B. $2$
• C. $3$
• D. $5$

Answer 1

Answer: (B)

$2si{n}^2\theta +3co{s}^2\theta$
$=2\left(si{n}^2\theta +co{s}^2\theta \right)+co{s}^2\theta$
$=2+co{s}^2\theta$
Least value of $co{s}^2\theta =0$
$\therefore$ least value of $25si{n}^2\theta +3co{s}^2\theta$
$=2+0=2$