Answer:
Option (b) is correct.
The expression \(\cos x + \tan x \sin x\) can be simplified to \(\sec x\)
Step-by-step explanation:
Given expression \(\cos x + \tan x \sin x\)
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,
\(\cos x + \tan x \sin x\)
We know, \(\tan x= \frac{\sin x}{\cos x}\)
Given expression becomes,
\(\cos x +\frac{\sin x}{\cos x} \sin x\)
Taking LCM, we get
\(\frac{\cos^2 x +\sin^2 x}{\cos x}\)
Also from trigonometric identity \(\sin^2 x+\cos^2 x=1\)
Expression becomes,
\(\frac{1}{\cos x}=\sec x\)
Thus, option (b) is correct.
The expression \(\cos x + \tan x \sin x\) can be simplified to \(\sec x\)
