Question

The least value of $3{\sin }^2\theta +4{\cos }^2\theta$is

• A. $2$
• B. $3$
• C. $0$
• D. $1$

Answer 1

The correct option is B

$3$

Solve the given expression

Given expression, $3{\sin }^2\theta +4{\cos }^2\theta$

$=3(1-{\cos }^2\theta )+4{\cos }^2\theta$ …$\mathbf{[}\mathbf{\because }\mathit{s}\mathit{i}{\mathit{n}}^{\mathbf{2}}\mathit{\theta }\mathbf{+}\mathit{c}\mathit{o}{\mathit{s}}^{\mathbf{2}}\mathit{\theta }\mathbf{=}\mathbf{1}\mathbf{]}$

$=3-3{\cos }^2\theta +4{\cos }^2\theta$

$=3+{\cos }^2\theta$ Now, the So, the minimum value will be obtained ,when the value of${\cos }^2\theta =0$

Therefore ,the least value of $3{\sin }^2\theta +{\cos }^2\theta =3$