Answer:
see explanation
Step-by-step explanation:
using the identities
• tan x = [tex]\frac{sinx}{cosx}[/tex] , cot x = [tex]\frac{cosx}{sinx}[/tex]
• sin²x + cos²x = 1
• csc x = [tex]\frac{1}{sinx}[/tex] , sec x = [tex]\frac{1}{cosx}[/tex]
Consider the left side
tan x + cot x
= [tex]\frac{sinx}{cosx}[/tex] + [tex]\frac{cosx}{sinx}[/tex]
= [tex]\frac{sin^2x+cos^2x}{cosxsinx}[/tex]
= [tex]\frac{1}{cosxsinx}[/tex]
= [tex]\frac{1}{sinx}[/tex] × [tex]\frac{1}{cosx}[/tex]
= csc x sec x
= right side , thus verified
