Question

Given that $\cos$ $\theta =\frac{1}{2}$, then the value of $\frac{2\sec \theta }{1+{\tan }^2\theta }$is

• A. $1$
• B. $2$
• C. $\frac{1}{2}$
• D. $0$

Answer 1

The correct option is A $1$

$\cos \theta =\frac{1}{2}$

$\Rightarrow \theta =60°$

$\Rightarrow \frac{2\sec \theta }{1+{\tan }^2\theta }=\frac{2\sec 60°}{1+{\tan }^{2}60°}=\frac{2\times 2}{1+{\left(\sqrt{3}\right)}^2}=\frac{4}{4}=1$

Hence, the answer is $1.$