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1 vote
The expression cosx + tanx sinx can be simplified to _____.

A. cosx sinx
B. secx
C. cotx
D. cscx

User Eagletech
by
8.3k points

2 Answers

4 votes

Answer:

Option (b) is correct.

The expression
\cos x + \tan x \sin x can be simplified to
\sec x

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= (\sin x)/(\cos x)

Given expression becomes,


\cos x +(\sin x)/(\cos x) \sin x

Taking LCM, we get


(\cos^2 x +\sin^2 x)/(\cos x)

Also from trigonometric identity
\sin^2 x+\cos^2 x=1

Expression becomes,


(1)/(\cos x)=\sec x

Thus, option (b) is correct.

The expression
\cos x + \tan x \sin x can be simplified to
\sec x

User Ziga Petek
by
8.2k points
3 votes

The expression cosx + tanx sinx can be simplified to secx. The correct answer between all the choices given is the second choice or letter B. I am hoping that this answer has satisfied your query about and it will be able to help you.

User Adam Matan
by
8.2k points
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