Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
secx = [tex]\frac{1}{cosx}[/tex] , cosecx = [tex]\frac{1}{sinx}[/tex]
cotx = [tex]\frac{cosx}{sinx}[/tex] , tanx = [tex]\frac{sinx}{cosx}[/tex]
Consider the left side
secA cosecA - cotA
= [tex]\frac{1}{cosA}[/tex] × [tex]\frac{1}{sinA}[/tex] - [tex]\frac{cosA}{sinA}[/tex]
= [tex]\frac{1}{cosAsinA}[/tex] - [tex]\frac{cosA}{sinA}[/tex]
= [tex]\frac{1-cos^2A}{cosAsinA}[/tex]
= [tex]\frac{sin^2A}{cosAsinA}[/tex] ( cancel sinA on numerator/ denominator )
= [tex]\frac{sinA}{cosA}[/tex]
= tanA = right side ⇒ proven
