# Find the Determinant [[1,0,sin(x)],[1,0,cos(x)],[1,sec(x),-sin(x)]]

Set up the determinant by breaking it into smaller components.
Since the matrix is multiplied by , the determinant is .
Since the matrix is multiplied by , the determinant is .
The determinant of is .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Rewrite in terms of sines and cosines.
Simplify each term.
Multiply by .
Rewrite as .
Simplify terms.
Apply the distributive property.
Cancel the common factor of .
Move the leading negative in into the numerator.
Cancel the common factor.
Rewrite the expression.
Multiply .
Multiply by .
Multiply by .
Combine and .
Convert from to .
Combine the opposite terms in .