Answer:
Option (b) is correct.
The expression [tex]\cos x + \tan x \sin x[/tex] can be simplified to [tex]\sec x[/tex]
Step-by-step explanation:
Given expression [tex]\cos x + \tan x \sin x[/tex]
We have to simplify the given expression and write it in simplified form and choose the correct option from the given options.
Consider the given expression,
[tex]\cos x + \tan x \sin x[/tex]
We know, [tex]\tan x= \frac{\sin x}{\cos x}[/tex]
Given expression becomes,
[tex]\cos x +\frac{\sin x}{\cos x} \sin x[/tex]
Taking LCM, we get
[tex]\frac{\cos^2 x +\sin^2 x}{\cos x}[/tex]
Also from trigonometric identity [tex]\sin^2 x+\cos^2 x=1[/tex]
Expression becomes,
[tex]\frac{1}{\cos x}=\sec x[/tex]
Thus, option (b) is correct.
The expression [tex]\cos x + \tan x \sin x[/tex] can be simplified to [tex]\sec x[/tex]
