( sec -1 )(sec +1 ) = ?
sec^2 -1
1/cos^2 - 1
1/cos^2 - cos^2/cos^2
sin^2/cos^2
tan^2
To find the value of (sec - 1)(sec + 1), we can start by expanding the expression using the distributive property.
(sec - 1)(sec + 1) = sec * sec + sec * 1 - 1 * sec - 1 * 1
Now, let's simplify each term:
sec * sec = sec^2 (since sec * sec = sec^2)
sec * 1 = sec (since anything multiplied by 1 remains unchanged)
-1 * sec = -sec (since a negative sign in front of a variable implies multiplication by -1)
-1 * 1 = -1 (since a negative sign multiplied by 1 is -1)
Now we can rewrite the expression with the simplified terms:
sec^2 + sec - sec - 1
Notice that "sec - sec" cancels each other out, so we're left with:
sec^2 - 1
Therefore, (sec - 1)(sec + 1) simplifies to sec^2 - 1.