Question

Can someone please help me

Answer 1

Right option is B.

Explanation:

`\sf \longrightarrow ( \sec x \sin( - x) + \tan( - x) )/(1 + \sec( - x) ) \\ \\ \sf \longrightarrow ( \sec x( - \sin x) - \tan x)/(1 + \sec x) \\ \\ \sf \longrightarrow ( - (1)/( \cos x ) * \sin x - \tan x )/(1 + \sec x) \\ \\ \sf \longrightarrow ( - \tan x - \tan x)/(1 + \sec x) \\ \\ \sf \longrightarrow ( - 2 \tan x)/(1 + \sec x) \\ \\ \sf \longrightarrow ( ( - 2 \sin x)/( \cos x) )/(1 + (1)/( \cos x) ) \\ \\ \sf \longrightarrow ( ( - 2 \sin x)/( \cos x) )/( ( \cos x + 1)/( \cos x) ) \\ \\ \boxed{ \sf{\longrightarrow ( - 2 \sin x)/( \cos x + 1) }}`