Question

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

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

Answer 1

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`

Answer 2

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.