Respuesta :

Answer:

B

Step-by-step explanation:

using the trigonometric identities

• cos x = [tex]\frac{1}{secx}[/tex], sin x = [tex]\frac{1}{cscx}[/tex]

• tan x = [tex]\frac{sinx}{cosx}[/tex], cot x = [tex]\frac{cosx}{sinx}[/tex]

the expression can be rewritten as

cos x([tex]\frac{sinx}{cosx}[/tex] + [tex]\frac{cosx}{sinx}[/tex])

distributing gives

sin x + [tex]\frac{cos^2x}{sinx}[/tex] ( expressing as a single fraction )

= [tex]\frac{sin^2x+cos^2x}{sinx}[/tex] = [tex]\frac{1}{sinx}[/tex] = csc x