Question

Choose the correct answer from the alternatives given.
If $\theta$ be an acute angle and 7 $si{n}^2\theta +3co{s}^2\theta$ = 4, then the value of tan$\theta$ is

• A. $\sqrt{3}$
• B. $\frac{1}{\sqrt{3}}$
• C. $1$
• D. $0$

Answer 1

The correct option is B $\frac{1}{\sqrt{3}}$

$7si{n}^2\theta +3co{s}^2\theta =4$
Dividing the equation by $co{s}^2\theta .$
$7\frac{si{n}^2\theta }{co{s}^2\theta }+3=\frac{4}{co{s}^2\theta }=4se{c}^2\theta$
$\Rightarrow 7ta{n}^2\theta +3=4(1+ta{n}^2\theta )\Rightarrow 7ta{n}^2\theta +3=4+4ta{n}^2\theta$
$\Rightarrow tan\theta =\frac{1}{\sqrt{3}}$