### Video Transcript

Evaluate the determinant of
negative four eight sec π negative sec π two tan squared π.

Remember these lines represent the
determinant of the matrix. For the matrix π΄, given by π, π,
π, π, its determinant is calculated by finding the product of elements π and π
and subtracting the product of π and π. Letβs apply this to the matrix
weβve been given.

The determinant of π΄ is negative
four times two tan squared π minus eight sec π times negative sec π. We can simplify our expression to
get negative eight tan squared π add eight sec squared π. We are next going to factorize our
expression to give us the determinant of π΄ equals eight multiplied by six squared
π minus tan squared π.

Then, in order to take this
further, we do need to recall our trigonometric identities. The one weβre interested in today
is tan squared π add one equals sec squared π. Letβs rearrange this formula to get
sec squared π minus tan squared π equals one. Weβve done this so we can replace
sec squared π minus tan squared π with one in our expression, leaving us with the
determinant of π΄ equals eight times one which is eight.

The determinant of our matrix is
eight.