Question

If $sec\theta +tan\theta =x,thensec\theta =$

• A. $\frac{x^2+1}{x}$
• B. $\frac{x^2+1}{2x}$
• C. $\frac{x^2-1}{2x}$
• D. $\frac{x^2-1}{x}$

Answer 1

The correct option is B

$\frac{x^2+1}{2x}$

$sec\theta +tan\theta =x$ ...... (1)
$Multiplysec\theta -tan\theta$ on both sides,
$(sec\theta +tan\theta )(sec\theta -tan\theta )=x(sec\theta -tan\theta )$
$1=x(sec\theta -tan\theta )$
$\Rightarrow sec\theta -tan\theta =\frac{1}{x}$ .....(2)

Adding equation (1) and (2) we get,
$\Rightarrow 2sec\theta =\frac{1}{x}+x$
$\Rightarrow sec\theta =\frac{x^2+1}{2x}$