Question

If $\tan \theta$=$\frac{1}{\sqrt{3}}$ what is the value of $7{\sin }^2\theta +3{\cos }^2\theta$?

• A. $10$
• B. $7$
• C. $4$
• D. $3$

Answer 1

The correct option is C $4$

$tan\theta =\frac{1}{\sqrt{3}}$

$\because tan{30}^{\circ }=\frac{1}{\sqrt{3}}$

$\therefore \theta ={30}^{\circ }$

Then the value of

$7si{n}^2\theta +3co{s}^2\theta \Rightarrow 7si{n}^2{30}^{\circ }+3co{s}^2{30}^{\circ }$

$\because sin{30}^{\circ }=\frac{1}{2}$ and $cos{30}^{\circ }=\frac{\sqrt{3}}{2}$

$\therefore 7\times (\frac{1}{2}{)}^2+3\times (\frac{\sqrt{3}}{2}{)}^2$

$\Rightarrow \frac{7}{4}+\frac{9}{4}=\frac{16}{4}=4$