Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
tan x = [tex]\frac{sinx}{cosx}[/tex], sin² x + cos²x = 1, sec x = [tex]\frac{1}{cosx}[/tex]
Consider the left side
- tant - [tex]\frac{cost}{sint-1}[/tex]
= - [tex]\frac{sint}{cost}[/tex] - [tex]\frac{cost}{sint-1}[/tex]
= [tex]\frac{-sint(sint-1)}{cost(sint-1)}[/tex] - [tex]\frac{cos^2t}{cost(sint-1)}[/tex]
= [tex]\frac{-sin^2t+sint-cos^2t}{cost(sint-1)}[/tex]
= [tex]\frac{-(sin^2t+cos^2t)+sint}{cost(sint-1)}[/tex]
= [tex]\frac{sint-1}{cost(sint-1)}[/tex] ← cancel (sint - 1) on numerator/ denominator
= [tex]\frac{1}{cost}[/tex]
= sect = right side ⇒ verified
