Answer:
see explanation
Step-by-step explanation:
Using the identities
tan x = [tex]\frac{sinx}{cosx}[/tex] , sec x = [tex]\frac{1}{cosx}[/tex] , csc x = [tex]\frac{1}{sinx}[/tex] , then consider left side
sinxcosxtanxsecxcscx
= sinxcosx × [tex]\frac{sinx}{cosx}[/tex] × secxcscx ← cancel cosx on numerator/ denominator
= sinx × sinx × [tex]\frac{1}{cosx}[/tex] × [tex]\frac{1}{sinx}[/tex] ← cancel sinx on numerator/ denominator
= sinx × [tex]\frac{1}{cosx}[/tex]
= [tex]\frac{sinx}{cosx}[/tex]
= tan x
= right side , thus proven
