Final answer:
To prove sec(x)-tan(x)sin(x) = 1/sec(x), we can rewrite the expression using the definitions of sec(x), tan(x), and sin(x), find a common denominator, and simplify.
Step-by-step explanation:
To prove the identity sec(x)-tan(x)sin(x) = 1/sec(x), we need to manipulate the expression on the left side to make it equivalent to the right side.
We can start by using the definitions of sec(x), tan(x), and sin(x) to rewrite the left side as (1/cos(x)) - (sin^2(x)/cos(x)).
Next, we can find a common denominator and combine the fractions, giving us (1 - sin^2(x))/cos(x). Since 1 - sin^2(x) = cos^2(x), we can simplify further to (cos^2(x))/cos(x), which reduces to cos(x).