Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
• tan x = [tex]\frac{sinx}{cosx}[/tex]
• sec x = [tex]\frac{1}{cosx}[/tex], csc x = [tex]\frac{1}{sinx}[/tex]
Consider the left side with x = Θ
[tex]\frac{sec^2x}{tanx}[/tex]
=[tex]\frac{1/cos^2x}{\frac{sinx}{cosx} }[/tex]
= [tex]\frac{1}{cos^2x}[/tex] × [tex]\frac{cosx}{sinx}[/tex]
= [tex]\frac{1}{cosxsinx}[/tex]
= [tex]\frac{1}{cosx}[/tex] × [tex]\frac{1}{sinx}[/tex]
= secxcscx = right side ⇒ verified
