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Verified Answer :

The best and most correct answer among the choices your question about trigonometric expressions provided is the first choice which is cos x.

cotx sinx - sin(π/2-x) + cosx 
= cosx/sinx * sinx - cosx + cosx 
= cosx - cosx + cosx 
= cosx

I hope it has come to your help.

Answer:

Option A

Step-by-step explanation:

Given expression: \(cotx\times sinx-sin(\frac{\pi }{2}-x)+cosx\)

Simplifying the expression :

\(cotx\times sinx-sin(\frac{\pi}{2}-x)+cosx\)  


applying property of trigonometry,

\(cotx=\frac{cosx}{sinx}\)   and   \(sin(\frac{\pi}{2}-x)=cosx\)

we get,

\(=\frac{cosx}{sinx}\times sinx-cosx+cosx\)  


\(=cosx-cosx+cosx\)


\(=cosx\)

Therefore, option A is correct

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