Answer:
Right option is B.
Step-by-step explanation:
[tex] \sf \longrightarrow \frac{ \sec x \sin( - x) + \tan( - x) }{1 + \sec( - x) } \\ \\ \sf \longrightarrow \frac{ \sec x( - \sin x) - \tan x}{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ - \frac{1}{ \cos x } \times \sin x - \tan x }{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ - \tan x - \tan x}{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ - 2 \tan x}{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ \frac{ - 2 \sin x}{ \cos x} }{1 + \frac{1}{ \cos x} } \\ \\ \sf \longrightarrow \frac{ \frac{ - 2 \sin x}{ \cos x} }{ \frac{ \cos x + 1}{ \cos x} } \\ \\ \boxed{ \sf{\longrightarrow \frac{ - 2 \sin x}{ \cos x + 1} }}[/tex]
