Respuesta :

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: [tex]cotx\times sinx-sin(\frac{\pi }{2}-x)+cosx[/tex]

Simplifying the expression :

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


applying property of trigonometry,

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

we get,

[tex]=\frac{cosx}{sinx}\times sinx-cosx+cosx[/tex]  


[tex]=cosx-cosx+cosx[/tex]


[tex]=cosx[/tex]

Therefore, option A is correct

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