Final answer:
To prove the identity (sec²(x)-1)cos(x)=sin²(x)sec(x), we simplify the left and right sides separately and show that they are equal.
Step-by-step explanation:
To prove the identity (sec²(x)-1)cos(x)=sin²(x)sec(x), we'll start with the left side of the equation:
(sec²(x)-1)cos(x) = (1/cos²(x) - 1)cos(x) = (1 - cos²(x))/cos(x)
Now, let's simplify the right side of the equation:
sin²(x)sec(x) = sin²(x) * (1/cos(x)) = sin²(x)/cos(x)
By simplifying both sides, it's clear that the left side is equal to the right side, proving the identity.
Learn more about Proving trigonometric identities