If cos x = 12/13 and x is an acute angle, then ​

Question

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

(a) \(\frac{\sqrt{115}}{12}\)

(b) \(\frac{\sqrt{116}}{12}\)

(c) \(\frac{\sqrt{119}}{12}\)

(d) \(\frac{\sqrt{117}}{12}\)

Answer 1

Correct option is (c) \(\frac{\sqrt{119}}{12}\) 

\(\cos x = \frac {12}{13}\) or \(\sec x = \frac{13}{12}\)

Now,