Question

Verify the identity.

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

tan x = $\frac{sinx}{cosx}$, sin² x + cos²x = 1, sec x = $\frac{1}{cosx}$

Consider the left side

- tant - $\frac{cost}{sint-1}$

= - $\frac{sint}{cost}$ - $\frac{cost}{sint-1}$

= $\frac{-sint(sint-1)}{cost(sint-1)}$ - $\frac{cos^2t}{cost(sint-1)}$

= $\frac{-sin^2t+sint-cos^2t}{cost(sint-1)}$

= $\frac{-(sin^2t+cos^2t)+sint}{cost(sint-1)}$

= $\frac{sint-1}{cost(sint-1)}$ ← cancel (sint - 1) on numerator/ denominator

= $\frac{1}{cost}$

= sect = right side ⇒ verified