Question

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

• 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 $\frac{\sqrt{119}}{12}$

$\cos x=\frac{12}{13}$ or $\sec x=\frac{13}{12}$
Now, $\sqrt{(1+\frac{\sin x}{\cos x})(1-\tan x)}$
= $\sqrt{(1+\tan x)(1-\tan x)}$
= $\sqrt{1-{\tan }^{2}x}$
= $\sqrt{1-{\sec }^{2}x+1}$
= $\sqrt{2-(\frac{13}{12}{)}^2}$
= $\sqrt{\frac{288-169}{144}}$
= $\frac{\sqrt{119}}{12}$