Question

If $\cos \theta =\frac{12}{13}$ and $\theta$ is an acute angle, then $\sqrt{(1+\frac{\sin \theta }{\cos \theta })(1-\tan \theta )}$ is :

• A. $\frac{\sqrt{115}}{12}$
• B. $\frac{\sqrt{116}}{12}$
• C. $\frac{\sqrt{119}}{12}$
• D. $\frac{\sqrt{117}}{12}$

Answer 1

The correct option is C $\frac{\sqrt{119}}{12}$

Given, $\cos \theta =\frac{12}{13}=\frac{b}{h}$

$\therefore p=\sqrt{{\left(13\right)}^2-{\left(12\right)}^2}=5$

$\therefore \sin \theta =\frac{p}{h}=\frac{5}{12},\tan \theta =\frac{p}{b}=\frac{5}{12}$

$\sqrt{(1+\tan \theta )(1-\tan \theta )}$

$=\sqrt{1-{\tan }^2\theta }$

$=\sqrt{1-\frac{25}{144}}$

$=\sqrt{\frac{119}{144}}$

$=\frac{\sqrt{119}}{12}$