Question

If $sec\theta -tan\theta =k,$ then the value of $sec\theta +tan\theta$ is

• A. $(1-k)$
• B. $(1+k)$
• C. $\frac{1}{k}$
• D. $1-\frac{1}{k}$

Answer 1

The correct option is C $\frac{1}{k}$

Given, $sec\theta -tan\theta =k................\left(i\right)$
Also, $se{c}^2\theta -ta{n}^2\theta =\mathrm{1.............}\left(ii\right)$
Dividing equation (ii) by (i), we get
$\frac{se{c}^2\theta -ta{n}^2\theta }{sec\theta -tan\theta }=\frac{1}{k}$
or $sec\theta +tan\theta =\frac{1}{k}$